Numerical solution, couette flow using crank nicolson implicit method
•Download as PPTX, PDF•
3 likes•4,666 views
Couette flow is the flow of a fluid between two parallel plates, where the lower plate is stationary and the upper plate is moving, creating shear stresses that drive the fluid flow. The document describes numerically solving the governing equations for Couette flow using the Crank-Nicolson technique, which involves discretizing the equations on a grid and solving the resulting tridiagonal matrix using methods like Thomas algorithm.
Report
Share
Report
Share
Recommended
Introduction to FEA
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
Finite element method (matlab) milan kumar rai
The document provides an overview of the finite element method (FEM). It explains that FEM involves dividing a structure into small pieces called finite elements and solving equations over each element. This allows solving complex problems by relating small, simple elements. The document outlines the basic steps of FEM, including discretization, deriving element equations, and provides an example of applying FEM to a 1D bar problem and 2D truss problem.
Finite element week 1
The document outlines a 16-week course on the finite element method (FEM). It introduces FEM and its applications in heat transfer, fluid mechanics, and solid mechanics. Over the course, students will learn how to formulate the finite element equation, create elements to model problems, and solve problems using FEM software. Assessment includes homework, programming tests, a midterm, and a final exam.
Introduction to fem
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
General steps of the finite element method
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
Finite Element Methods
The document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
FEM: Introduction and Weighted Residual Methods
What are weighted residual methods?
How to apply Galerkin Method to the finite element model?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/TopicX+Approximate+Methods+-+Weighted+Residual+Methods
Contact stresses
Contact stresses occur where two solid bodies are pressed together over a limited contact area. They are important because failures often initiate at contact surfaces due to high cyclic stresses. Contact stresses are computed using elasticity equations that assume homogenous, isotropic materials and an elliptical contact patch shape. The maximum principal stress is largest in magnitude and occurs at the contact surface, while maximum shear stress occurs just below the surface. Orthogonal shear stresses on planes parallel to the contact are also significant for fatigue failure analysis. Line contact problems have different equations from point contact due to the contact geometry.
Recommended
Introduction to FEA
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
Finite element method (matlab) milan kumar rai
The document provides an overview of the finite element method (FEM). It explains that FEM involves dividing a structure into small pieces called finite elements and solving equations over each element. This allows solving complex problems by relating small, simple elements. The document outlines the basic steps of FEM, including discretization, deriving element equations, and provides an example of applying FEM to a 1D bar problem and 2D truss problem.
Finite element week 1
The document outlines a 16-week course on the finite element method (FEM). It introduces FEM and its applications in heat transfer, fluid mechanics, and solid mechanics. Over the course, students will learn how to formulate the finite element equation, create elements to model problems, and solve problems using FEM software. Assessment includes homework, programming tests, a midterm, and a final exam.
Introduction to fem
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
General steps of the finite element method
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
Finite Element Methods
The document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
FEM: Introduction and Weighted Residual Methods
What are weighted residual methods?
How to apply Galerkin Method to the finite element model?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/TopicX+Approximate+Methods+-+Weighted+Residual+Methods
Contact stresses
Contact stresses occur where two solid bodies are pressed together over a limited contact area. They are important because failures often initiate at contact surfaces due to high cyclic stresses. Contact stresses are computed using elasticity equations that assume homogenous, isotropic materials and an elliptical contact patch shape. The maximum principal stress is largest in magnitude and occurs at the contact surface, while maximum shear stress occurs just below the surface. Orthogonal shear stresses on planes parallel to the contact are also significant for fatigue failure analysis. Line contact problems have different equations from point contact due to the contact geometry.
Finite difference equation
This document discusses heat transfer through conduction and various methods for solving the heat equation using finite difference approximations. It introduces the heat equation in Cartesian, cylindrical and spherical coordinates. It discusses boundary conditions and describes setting up a nodal network to discretize the domain. It then presents the finite difference form of the heat equation and describes different cases for nodal finite difference equations, including for interior nodes, nodes at corners or surfaces with convection, and nodes at surfaces with uniform heat flux. It discusses solving the finite difference equations using matrix inversion, Gauss-Seidel iteration, and provides examples.
Unit 1 notes-final
The document provides an introduction to the Finite Element Method (FEM). It discusses the history and development of FEM from the 1950s to the present. It outlines the basic concepts of FEM including discretization of the domain into finite elements connected at nodes, and the approximation of displacements within each element. The document also discusses minimum potential energy theory, which is the variational principle that FEM is based on. Example problems and a tutorial are mentioned. Advantages of FEM include its ability to model complex geometries and loading, while disadvantages include increased computational time and memory requirements compared to other methods.
Finite Element Method
The document discusses the finite element method (FEM) for analyzing beam structures. FEM involves subdividing a structure into finite elements of simple shape and solving for the whole structure. Elements can be one-, two-, or three-dimensional, with accuracy increasing with more elements. Nodes are points where elements connect, and nodal displacements describe element deformation. FEM allows analyzing complex shapes like plates by treating them as assemblies of beams. A simple bar analysis example demonstrates deriving and solving the stiffness matrix to determine displacements and forces from applied loads.
Introduction to finite element analysis
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
Introduction to Computational Fluid Dynamics (CFD)
This document provides an overview of computational fluid dynamics (CFD). It defines CFD as using computer simulations to predict fluid flow phenomena by modeling continuous fluids with partial differential equations. The document outlines where CFD is used in various industries like aerospace, automotive, biomedical, and more. It also discusses the physics, modeling, numerics, and overall CFD process involved in simulations. Examples are given of mesh generation and CFD being used to analyze problems like bottle filling.
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMS
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
Ch 12 unconventional machining
The document discusses electrochemical machining (ECM). ECM is an unconventional machining process where material is removed from a workpiece made of an electrically conductive material via an electrochemical reaction. In ECM, the workpiece acts as an anode in an electrolyte solution, and a tool acts as a cathode. A direct current is passed between them, causing metal ions from the workpiece to dissolve into the electrolyte solution. ECM can machine complex shapes with high accuracy and no tool wear. It has the highest material removal rate of any unconventional machining process but requires expensive equipment and a conductive workpiece material.
A brief introduction to finite difference method
The document provides a brief introduction to the finite difference method for numerically solving ordinary and partial differential equations.
It explains that finite difference methods work by (1) discretizing the domain into a grid, (2) approximating derivatives at each grid point using finite difference formulas like forward, backward or central differences, and (3) reducing the differential equation to a system of algebraic equations that can be solved numerically. Examples are given for applying finite differences to first order ODEs, second order PDEs, and higher order equations.
concept of Actuators
This document discusses different types of actuators. An actuator is a device that converts a control signal into mechanical motion. There are several types of actuators including hydraulic, pneumatic, electric, thermal, and mechanical. Hydraulic actuators use fluid pressure to generate motion, while pneumatic actuators use compressed air. Electric actuators convert electrical energy into motion through motors or electrohydraulic systems. Thermal and magnetic actuators use heat or magnetism to trigger materials like shape memory alloys. Mechanical actuators convert one type of motion into another using components like gears and rails.
DEGREE OF FREEDOM OF A KINEMATIC MECHANISM
The document discusses degrees of freedom (DOF) of rigid bodies and kinematic mechanisms. It states that a rigid body in 3D space has 6 DOF, while in a 2D plane it has 3 DOF consisting of translations along two axes and a rotation. For mechanisms, DOF is calculated using formulas that account for the number of links, joints, and their types. DOF indicates the number of independent motions a mechanism can perform, with higher values indicating less constraint. Formulas to calculate DOF in 2D and 3D are provided along with examples worked out.
Finite element method
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
Chemical machining
Chemical machining is a nontraditional machining process that removes metal from a workpiece by immersing it in a chemical solution. The process involves masking areas of the workpiece to be protected, then etching away the exposed material with an acidic or alkaline solution. Chemical machining can produce complex parts with close tolerances and is used for applications such as MEMS and semiconductor devices that require micro-scale features. The key steps of chemical machining include cleaning the workpiece, applying a photoresist mask, exposing the mask to create the desired pattern, etching, and removing the mask.
Introduction to finite element method(fem)
it tells u what is finite element method and it's use in solving typical 1D, 2D rods along with some soved problems .
A Study Of BVP4C Method For Solving Boundary.pptx
This document discusses the BVP4C method for solving boundary value problems (BVPs) using MATLAB. It begins with an introduction to differential equations, order, degree, and methods for solving first order equations. It then describes the BVP4C method, including defining the ODE function, boundary conditions function, initial guess, and mesh. As an example, it solves a second order nonlinear BVP and compares solutions using different initial guesses. Finally, it addresses using BVP4C to solve beam deflection problems.
CFD & ANSYS FLUENT
This document provides an introduction to computational fluid dynamics (CFD) and the use of ANSYS FLUENT software. It discusses the basics of fluid dynamics and how CFD solves fluid flow problems using numerical methods. It also outlines the steps to set up and solve a problem in ANSYS FLUENT, including pre-processing, defining the physical problem, running the simulation, and analyzing results. The document serves as a brief overview of CFD concepts and capabilities for engineering applications.
Slip Line Field Method - Presentation
Slip line field method and its application in forming process
Manufacturing Process Class - Final year
Micro Electrochemical Machining
Micro electrochemical machining (Micro ECM) is a non-traditional machining process that uses electrolysis to remove material from a workpiece in micro-scale dimensions. It works by applying a voltage between a tool cathode and workpiece anode separated by an electrolyte, which causes the workpiece material to dissolve atom by atom according to Faraday's laws of electrolysis. Micro ECM has advantages over traditional machining for micro-scale applications and can machine complex micro-scale features with high precision and no thermal effects. Key parameters that affect the micro ECM process include inter-electrode gap, tool feed rate, electrolyte type and flow, and applied voltage.
Computational fluid dynamics (cfd)
Computational fluid dynamics (CFD) is the use of computing to simulate fluid flow, heat transfer, and other related phenomena. CFD works by numerically solving the governing equations of fluid dynamics. It allows for analyzing flows that are difficult to study experimentally. CFD has various applications in fields like aerospace, automotive, biomedical, and power generation. The CFD process involves discretizing the domain, applying initial and boundary conditions, numerically solving the governing equations, and post-processing the results. Common discretization methods are finite volume, finite element, and finite difference methods. CFD provides insight into flows and heat transfer while being faster and cheaper than physical experiments.
Me2353 finite-element-analysis-lecture-notes
This document outlines the contents and concepts of a course on finite element analysis. It covers fundamental concepts like discretization, matrix algebra, and weighted residual methods. It also covers one-dimensional problems involving bars, beams, and trusses. Shape functions, stiffness matrices, and finite element equations are derived for one-dimensional elements. Two-dimensional problems involving plane stress, strain, and heat transfer are also introduced. Numerical integration techniques are discussed. A variety of finite element applications are listed including structural and non-structural problems.
Application of Boundary Conditions to Obtain Better FEA Results
This document discusses applying proper boundary conditions in finite element analysis to obtain better results. It covers:
1) Typical boundary conditions like supports, connections, and structural symmetry to model structures accurately
2) Examples show boundary conditions significantly affect results like displacements and moments
3) Nonlinear behaviors from large deformations, materials, and contact require special boundary conditions in analysis
Types of fluid flow best ppt
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
Couette Flow Velocity Profile Analysis
The computational fluid dynamics analysis calculated the Couette flow velocity profiles and Reynolds numbers for air, oil, and glycerine. It found that fluids with lower Reynolds numbers, primarily caused by higher dynamic viscosity, reached steady state velocity values faster. Specifically, glycerine reached steady state the fastest at 0.0567 seconds, followed by oil at 0.162 seconds, with air having the longest time of 4.62 seconds to reach steady state.
More Related Content
What's hot
Finite difference equation
This document discusses heat transfer through conduction and various methods for solving the heat equation using finite difference approximations. It introduces the heat equation in Cartesian, cylindrical and spherical coordinates. It discusses boundary conditions and describes setting up a nodal network to discretize the domain. It then presents the finite difference form of the heat equation and describes different cases for nodal finite difference equations, including for interior nodes, nodes at corners or surfaces with convection, and nodes at surfaces with uniform heat flux. It discusses solving the finite difference equations using matrix inversion, Gauss-Seidel iteration, and provides examples.
Unit 1 notes-final
The document provides an introduction to the Finite Element Method (FEM). It discusses the history and development of FEM from the 1950s to the present. It outlines the basic concepts of FEM including discretization of the domain into finite elements connected at nodes, and the approximation of displacements within each element. The document also discusses minimum potential energy theory, which is the variational principle that FEM is based on. Example problems and a tutorial are mentioned. Advantages of FEM include its ability to model complex geometries and loading, while disadvantages include increased computational time and memory requirements compared to other methods.
Finite Element Method
The document discusses the finite element method (FEM) for analyzing beam structures. FEM involves subdividing a structure into finite elements of simple shape and solving for the whole structure. Elements can be one-, two-, or three-dimensional, with accuracy increasing with more elements. Nodes are points where elements connect, and nodal displacements describe element deformation. FEM allows analyzing complex shapes like plates by treating them as assemblies of beams. A simple bar analysis example demonstrates deriving and solving the stiffness matrix to determine displacements and forces from applied loads.
Introduction to finite element analysis
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
Introduction to Computational Fluid Dynamics (CFD)
This document provides an overview of computational fluid dynamics (CFD). It defines CFD as using computer simulations to predict fluid flow phenomena by modeling continuous fluids with partial differential equations. The document outlines where CFD is used in various industries like aerospace, automotive, biomedical, and more. It also discusses the physics, modeling, numerics, and overall CFD process involved in simulations. Examples are given of mesh generation and CFD being used to analyze problems like bottle filling.
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMS
This report provides a practical overview of numerical solutions to the heat equation using the finite difference method (FDM). The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation. Complete, working Matlab and FORTRAN codes for each program are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated. These sample calculations show that the schemes realize theoretical predictions of how their truncation errors depend on mesh spacing and time step. The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS). The codes also allow us to experiment with the stability limit of the FTCS scheme.
Ch 12 unconventional machining
The document discusses electrochemical machining (ECM). ECM is an unconventional machining process where material is removed from a workpiece made of an electrically conductive material via an electrochemical reaction. In ECM, the workpiece acts as an anode in an electrolyte solution, and a tool acts as a cathode. A direct current is passed between them, causing metal ions from the workpiece to dissolve into the electrolyte solution. ECM can machine complex shapes with high accuracy and no tool wear. It has the highest material removal rate of any unconventional machining process but requires expensive equipment and a conductive workpiece material.
A brief introduction to finite difference method
The document provides a brief introduction to the finite difference method for numerically solving ordinary and partial differential equations.
It explains that finite difference methods work by (1) discretizing the domain into a grid, (2) approximating derivatives at each grid point using finite difference formulas like forward, backward or central differences, and (3) reducing the differential equation to a system of algebraic equations that can be solved numerically. Examples are given for applying finite differences to first order ODEs, second order PDEs, and higher order equations.
concept of Actuators
This document discusses different types of actuators. An actuator is a device that converts a control signal into mechanical motion. There are several types of actuators including hydraulic, pneumatic, electric, thermal, and mechanical. Hydraulic actuators use fluid pressure to generate motion, while pneumatic actuators use compressed air. Electric actuators convert electrical energy into motion through motors or electrohydraulic systems. Thermal and magnetic actuators use heat or magnetism to trigger materials like shape memory alloys. Mechanical actuators convert one type of motion into another using components like gears and rails.
DEGREE OF FREEDOM OF A KINEMATIC MECHANISM
The document discusses degrees of freedom (DOF) of rigid bodies and kinematic mechanisms. It states that a rigid body in 3D space has 6 DOF, while in a 2D plane it has 3 DOF consisting of translations along two axes and a rotation. For mechanisms, DOF is calculated using formulas that account for the number of links, joints, and their types. DOF indicates the number of independent motions a mechanism can perform, with higher values indicating less constraint. Formulas to calculate DOF in 2D and 3D are provided along with examples worked out.
Finite element method
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
Chemical machining
Chemical machining is a nontraditional machining process that removes metal from a workpiece by immersing it in a chemical solution. The process involves masking areas of the workpiece to be protected, then etching away the exposed material with an acidic or alkaline solution. Chemical machining can produce complex parts with close tolerances and is used for applications such as MEMS and semiconductor devices that require micro-scale features. The key steps of chemical machining include cleaning the workpiece, applying a photoresist mask, exposing the mask to create the desired pattern, etching, and removing the mask.
Introduction to finite element method(fem)
it tells u what is finite element method and it's use in solving typical 1D, 2D rods along with some soved problems .
A Study Of BVP4C Method For Solving Boundary.pptx
This document discusses the BVP4C method for solving boundary value problems (BVPs) using MATLAB. It begins with an introduction to differential equations, order, degree, and methods for solving first order equations. It then describes the BVP4C method, including defining the ODE function, boundary conditions function, initial guess, and mesh. As an example, it solves a second order nonlinear BVP and compares solutions using different initial guesses. Finally, it addresses using BVP4C to solve beam deflection problems.
CFD & ANSYS FLUENT
This document provides an introduction to computational fluid dynamics (CFD) and the use of ANSYS FLUENT software. It discusses the basics of fluid dynamics and how CFD solves fluid flow problems using numerical methods. It also outlines the steps to set up and solve a problem in ANSYS FLUENT, including pre-processing, defining the physical problem, running the simulation, and analyzing results. The document serves as a brief overview of CFD concepts and capabilities for engineering applications.
Slip Line Field Method - Presentation
Slip line field method and its application in forming process
Manufacturing Process Class - Final year
Micro Electrochemical Machining
Micro electrochemical machining (Micro ECM) is a non-traditional machining process that uses electrolysis to remove material from a workpiece in micro-scale dimensions. It works by applying a voltage between a tool cathode and workpiece anode separated by an electrolyte, which causes the workpiece material to dissolve atom by atom according to Faraday's laws of electrolysis. Micro ECM has advantages over traditional machining for micro-scale applications and can machine complex micro-scale features with high precision and no thermal effects. Key parameters that affect the micro ECM process include inter-electrode gap, tool feed rate, electrolyte type and flow, and applied voltage.
Computational fluid dynamics (cfd)
Computational fluid dynamics (CFD) is the use of computing to simulate fluid flow, heat transfer, and other related phenomena. CFD works by numerically solving the governing equations of fluid dynamics. It allows for analyzing flows that are difficult to study experimentally. CFD has various applications in fields like aerospace, automotive, biomedical, and power generation. The CFD process involves discretizing the domain, applying initial and boundary conditions, numerically solving the governing equations, and post-processing the results. Common discretization methods are finite volume, finite element, and finite difference methods. CFD provides insight into flows and heat transfer while being faster and cheaper than physical experiments.
Me2353 finite-element-analysis-lecture-notes
This document outlines the contents and concepts of a course on finite element analysis. It covers fundamental concepts like discretization, matrix algebra, and weighted residual methods. It also covers one-dimensional problems involving bars, beams, and trusses. Shape functions, stiffness matrices, and finite element equations are derived for one-dimensional elements. Two-dimensional problems involving plane stress, strain, and heat transfer are also introduced. Numerical integration techniques are discussed. A variety of finite element applications are listed including structural and non-structural problems.
Application of Boundary Conditions to Obtain Better FEA Results
This document discusses applying proper boundary conditions in finite element analysis to obtain better results. It covers:
1) Typical boundary conditions like supports, connections, and structural symmetry to model structures accurately
2) Examples show boundary conditions significantly affect results like displacements and moments
3) Nonlinear behaviors from large deformations, materials, and contact require special boundary conditions in analysis
What's hot (20)
Introduction to Computational Fluid Dynamics (CFD)
Introduction to Computational Fluid Dynamics (CFD)
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMS
FINITE DIFFERENCE MODELLING FOR HEAT TRANSFER PROBLEMS
Application of Boundary Conditions to Obtain Better FEA Results
Application of Boundary Conditions to Obtain Better FEA Results
Viewers also liked
Types of fluid flow best ppt
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
Couette Flow Velocity Profile Analysis
The computational fluid dynamics analysis calculated the Couette flow velocity profiles and Reynolds numbers for air, oil, and glycerine. It found that fluids with lower Reynolds numbers, primarily caused by higher dynamic viscosity, reached steady state velocity values faster. Specifically, glycerine reached steady state the fastest at 0.0567 seconds, followed by oil at 0.162 seconds, with air having the longest time of 4.62 seconds to reach steady state.
Thomas algorithm
1. Thomas' algorithm, also called the tridiagonal matrix algorithm (TDMA), is used to solve systems of equations with a tridiagonal matrix structure.
2. It works by applying Gaussian elimination to convert the system of equations into an upper triangular system that can then be solved using backward substitution.
3. An example problem demonstrating the algorithm is worked through, showing the conversion to upper triangular form and solution via backward substitution.
Different experimental techniques for solar flux
The document describes several experimental techniques for measuring solar flux density, including direct and indirect methods. Indirect methods use cameras to measure reflected light from a target, while direct methods use sensors mounted on a moving bar. Specific techniques are discussed, such as using a moving bar target and camera, stationary stripe targets with a moving focus, and stationary sensors. The PHLUX method is also described, which uses camera images and calibration to determine flux density on a receiver surface without additional sensors. Overall the document provides an overview of different experimental approaches for measuring solar flux and details key techniques.
Cholesky method and Thomas
This document discusses two methods for solving linear equations: the Thomas method and the Cholesky method. It provides examples of applying each method.
The Thomas method emerges from an LU factorization of a tridiagonal matrix. It involves forward and backward substitution to solve for the vector x given Ax=b.
The Cholesky method applies to positive definite symmetric matrices and factors the matrix A as A=LLT using an upper triangular matrix L. It involves solving Ly=b and LTx=y to solve Ax=b. An example shows applying the Cholesky method to decompose a symmetric matrix.
Fluid mechanics
This document discusses laminar and turbulent fluid flow in pipes. It defines laminar flow as smooth, ordered motion of fluid layers and turbulent flow as irregular motion with velocity fluctuations. The Reynolds number determines the flow regime, with laminar flow below 2000 and turbulent flow above 4000. For fully developed laminar pipe flow, the velocity profile is parabolic and the pressure drop is proportional to flow rate, pipe length, and fluid viscosity, inversely proportional to pipe diameter raised to the fourth power.
Fluid mechanics
Fluid mechanics deals with the behavior of fluids at rest and in motion. It can be divided into three divisions: hydrostatics, kinematics, and dynamics. Hydrostatics studies fluids at rest, kinematics deals with fluid motion without forces, and dynamics relates velocities, accelerations, and forces acting on fluids. Fluids include liquids and gases, with gases being readily compressible and liquids being nearly incompressible. Fluid mechanics has many applications in daily life and engineering.
Viewers also liked (7)
Similar to Numerical solution, couette flow using crank nicolson implicit method
MSc Presentation.potx
This document provides an overview of a thesis that used OpenFOAM to simulate unsteady aerodynamic flow over a sphere. The study aimed to analyze flow instabilities and quantify uncertainty in simulations. It used an IDDES turbulence model on refined meshes. Frequency analysis revealed peaks from vortex shedding and shear layer instabilities. Mean flow parameters matched experimental data. Future work could include hybrid RANS-LES models and longer simulations for improved flow statistics.
paper term SUMMARY powerpoint.pptx
TWO-STAGE SYSTEM IDENTIFICATION APPROACH FOR THREE DIMENSIONAL STRUCTURE SYSTEMS SUMMARY " hASAN kATKHUDA PAPER"
Presentation- thesis- Chaofan ZHANG
Presentation of my Ph.D. work on the Improvement of the Near Wall Treatment in Large Eddy Simulation for Aeroacoustic Applications
Multiple Resonant Multiconductor Transmission line Resonator Design using Cir...
The document presents techniques for designing multiple resonant multiconductor transmission line resonators. It discusses analyzing port admittance matrices using block matrix algebra methods like the 2n-port method and reduced dimension method. These methods decompose large port matrices into smaller matrices to efficiently determine resonance conditions. The document reviews existing multiconductor transmission line resonator designs and motivates developing analytical models for their resonance conditions.
"Reduction of uncertainties associated to the dynamic response of a ship unlo...
Here, the TRUSS (Training in Reducing Uncertainty in Structural Safety) ITN (Innovative Training Network) Horizon 2020 project (http://trussitn.eu, 2015-19) demonstrates how the accuracy of residual life assessment predictions can be improved by achieving a good agreement between measured and predicted dynamic responses of a crane structure. Existing records of measured strain data are often missing information such as the weight of the payload, the hoisting speed and acceleration that are relevant for structural assessment purposes. This paper aims to reduce uncertainties associated with the recorded data in an aged grab ship unloader by comparing measured and non-linear transient finite element analyses results for a loading/unloading cycle. The speed pattern is determined from a best match to the measured record. The moving load consisting of ‘trolley + grab + payload’ is modelled with parameters that are derived from minimizing differences between measured and simulated responses. The determination of these loading parameters is central to accurately assess the remaining life of ship unloaders.
Flujo turbulento
1. The document discusses laminar and turbulent fluid flow. Laminar flow is perfectly ordered while turbulent flow is chaotic with particles moving disorderly and forming eddies.
2. Characteristics of turbulent flow include irregularity, diffusivity, rotationality, and dissipation. Reynolds number, boundary layer, continuity equation, and equations like Bernoulli's are also covered.
3. Applications in petrochemical industry like well completion, production logging, drilling fluids, and production are mentioned. Microscales of Kolmogorov and heat transfer coefficients are also summarized.
Mri gradient coils
Gradient coils are used in MRI to spatially encode the MRI signal by creating linear magnetic field gradients in the x, y, and z directions. They are made of conducting loops or strips arranged in patterns like fingerprints that produce calibrated distortions of the main magnetic field. Modern scanners typically use distributed windings in copper sheets etched into complex patterns. Gradient coils are driven by powerful gradient amplifiers and require cooling to handle the heat from switching high currents rapidly. Proper gradient design and performance is crucial for achieving good spatial resolution and image quality in MRI.
posterformicrofluidics
1) The document describes simulations of two-phase fluid flow through a microfluidic snake channel using COMSOL Multiphysics to analyze inertial effects.
2) Two mathematical methods were used - Finite Element Method (FEM) and Level Set Method (LSM) - to simulate the Navier-Stokes equations governing fluid flow.
3) Results showed that even extremely laminar flow experienced instabilities due to inertial effects, proving that laminar flow can experience chaotic behavior in microchannels.
A two equation VLES turbulence model with near-wall delayed behaviour
This document introduces a new delayed two-equation very large eddy simulation (VLES) turbulence model. The VLES model was evaluated on simulations of flow over a square cylinder and a rudimentary landing gear. For the square cylinder, the VLES model captured key flow structures on coarse meshes and showed good agreement with experimental drag and lift data. For the landing gear, VLES showed favorable agreement with experimental surface pressures and drag data compared to other simulations, though lift prediction was poorer. The VLES model proved efficient compared to URANS, DES, and LES in initial tests.
Similar to Numerical solution, couette flow using crank nicolson implicit method (9)
Multiple Resonant Multiconductor Transmission line Resonator Design using Cir...
Multiple Resonant Multiconductor Transmission line Resonator Design using Cir...
"Reduction of uncertainties associated to the dynamic response of a ship unlo...
"Reduction of uncertainties associated to the dynamic response of a ship unlo...
A two equation VLES turbulence model with near-wall delayed behaviour
A two equation VLES turbulence model with near-wall delayed behaviour
Recently uploaded
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
Building Production Ready Search Pipelines with Spark and Milvus
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
Removing Uninteresting Bytes in Software Fuzzing
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...Edge AI and Vision Alliance
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.Microsoft - Power Platform_G.Aspiotis.pdf
Revolutionizing Application Development
with AI-powered low-code, presentation by George Aspiotis, Sr. Partner Development Manager, Microsoft
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
HCL Notes and Domino License Cost Reduction in the World of DLAU
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
UiPath Test Automation using UiPath Test Suite series, part 6
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
Communications Mining Series - Zero to Hero - Session 1
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
Presentation of the OECD Artificial Intelligence Review of Germany
Consult the full report at https://www.oecd.org/digital/oecd-artificial-intelligence-review-of-germany-609808d6-en.htm
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
Essentials of Automations: The Art of Triggers and Actions in FME
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
Video Streaming: Then, Now, and in the Future
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Recently uploaded (20)
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for Life Science to increase LLM accuracy
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Building Production Ready Search Pipelines with Spark and Milvus
Building Production Ready Search Pipelines with Spark and Milvus
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU
UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Communications Mining Series - Zero to Hero - Session 1
Communications Mining Series - Zero to Hero - Session 1
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
Essentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FME
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Numerical solution, couette flow using crank nicolson implicit method
- 1. NUMERICAL SOLUTION OF COUETTE FLOW USING CRANK NICOLSON TECHNIQUE MANOJKUMAR MAURYA M.E. 13906
- 2. DEFINATION • It is a flow between two parallel plates in which the lower plate is at rest while the upper plate is moving. • The plates are considered to be infinitely long • The flow field is driven by the shear stress exerted on fluid due to the movement of the upper plate.
- 7. Crank Nicolson technique, the finite difference representation
- 8. • We get different equations as we apply this equation at different grid points • The order of the matrix depends upon the number of grid points taken into consideration • The matrix thus obtained is tridiagonal matrix which is converted into bidiagonal form using Thomas algorithm or Gauss elimination method
- 10. Representation of tridiagonal matrix
- 11. Thomas algorithm