This document provides an introduction to computational fluid dynamics (CFD). It discusses what CFD is, why it is used, where it is applied, the modeling and numerical methods involved. CFD involves modeling fluid engineering systems using mathematical equations and numerical methods to discretize and solve the equations. It is used for analysis and design across many industries as a more cost effective alternative to experimental fluid dynamics. The document outlines the basic CFD process and provides examples of modeling turbulent flow and free surface flows.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
The Powerpoint presentation discusses about the Introduction to CFD and its Applications in various fields as an Introductory topic for Mechanical Engg. Students in General.
This document outlines the key steps in a typical computational fluid dynamics (CFD) analysis:
1) Define modeling goals and assumptions
2) Identify the domain to be modeled
3) Create a geometric model of the domain
4) Design and create a mesh of the domain
5) Set up the solver with appropriate physical models and boundary conditions
6) Compute the solution by solving the governing equations
7) Examine the results to validate the solution and extract useful data
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.
This document provides guidelines for modeling fluid flow simulations using ANSYS Fluent. It discusses defining modeling goals, pre-processing steps like geometry simplification and meshing, setting up the solver by selecting physical models and boundary conditions, computing the solution, and examining results. Guidelines are provided for choosing pressure-based vs density-based solvers, spatial and temporal discretization, and modeling turbulence. The document aims to help users optimize their workflow and achieve accurate results efficiently.
Computational fluid dynamics (CFD) is a numerical method used to analyze and solve fluid flow problems. CFD uses the mathematical equations that govern fluid motion and heat transfer to simulate the behavior of fluids. It provides a comprehensive examination of systems through modeling of velocity, pressure, temperature, and other properties without extensive physical testing. CFD has advantages of being relatively low cost, fast, and able to simulate real conditions. Limitations include accuracy depending on physical models and numerical errors from discretization. CFD is commonly used in engineering applications like aerodynamics, automotive, and electronics design.
This document provides notes for an introduction to computational fluid dynamics (CFD) course. It outlines the course organization, learning objectives, and contents. The key points are:
- The course grade is based on homeworks, a report, and a final exam. Interaction is extremely important.
- The learning objectives are to understand the role of C programming in fluid dynamics and numerical methods, learn various CFD terminology and best practices, and be able to set up and analyze simple aerodynamic problems.
- The contents include introductions to partial differential equations, finite difference methods, grids/boundaries, Euler/RANS equations, and case studies. Hands-on lab sessions make up a large part of
Computational fluid dynamics (CFD) is the use of numerical methods and algorithms to solve and analyze problems involving fluid flows. CFD allows engineers to simulate fluid flow, heat transfer, and other related physical processes. It provides a virtual laboratory for testing new designs without building physical prototypes. CFD is used across many industries like aerospace, automotive, biomedical, and more. It complements experimental testing by reducing costs and providing comprehensive flow field data. The document discusses the basics of CFD including discretization methods like finite difference and finite volume, common boundary conditions, and where CFD is applied.
This document discusses computational fluid dynamics (CFD). CFD uses numerical analysis and algorithms to solve and analyze fluid flow problems. It can be used at various stages of engineering to study designs, develop products, optimize designs, troubleshoot issues, and aid redesign. CFD complements experimental testing by reducing costs and effort required for data acquisition. It involves discretizing the fluid domain, applying boundary conditions, solving equations for conservation of properties, and interpolating results. Turbulence models and discretization methods like finite volume are discussed. The CFD process involves pre-processing the problem, solving it, and post-processing the results.
The Powerpoint presentation discusses about the Introduction to CFD and its Applications in various fields as an Introductory topic for Mechanical Engg. Students in General.
This document outlines the key steps in a typical computational fluid dynamics (CFD) analysis:
1) Define modeling goals and assumptions
2) Identify the domain to be modeled
3) Create a geometric model of the domain
4) Design and create a mesh of the domain
5) Set up the solver with appropriate physical models and boundary conditions
6) Compute the solution by solving the governing equations
7) Examine the results to validate the solution and extract useful data
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.
This document provides guidelines for modeling fluid flow simulations using ANSYS Fluent. It discusses defining modeling goals, pre-processing steps like geometry simplification and meshing, setting up the solver by selecting physical models and boundary conditions, computing the solution, and examining results. Guidelines are provided for choosing pressure-based vs density-based solvers, spatial and temporal discretization, and modeling turbulence. The document aims to help users optimize their workflow and achieve accurate results efficiently.
Computational fluid dynamics (CFD) is a numerical method used to analyze and solve fluid flow problems. CFD uses the mathematical equations that govern fluid motion and heat transfer to simulate the behavior of fluids. It provides a comprehensive examination of systems through modeling of velocity, pressure, temperature, and other properties without extensive physical testing. CFD has advantages of being relatively low cost, fast, and able to simulate real conditions. Limitations include accuracy depending on physical models and numerical errors from discretization. CFD is commonly used in engineering applications like aerodynamics, automotive, and electronics design.
This document provides notes for an introduction to computational fluid dynamics (CFD) course. It outlines the course organization, learning objectives, and contents. The key points are:
- The course grade is based on homeworks, a report, and a final exam. Interaction is extremely important.
- The learning objectives are to understand the role of C programming in fluid dynamics and numerical methods, learn various CFD terminology and best practices, and be able to set up and analyze simple aerodynamic problems.
- The contents include introductions to partial differential equations, finite difference methods, grids/boundaries, Euler/RANS equations, and case studies. Hands-on lab sessions make up a large part of
Computational fluid dynamics (CFD) is the use of numerical methods and algorithms to solve and analyze problems involving fluid flows. CFD allows engineers to simulate fluid flow, heat transfer, and other related physical processes. It provides a virtual laboratory for testing new designs without building physical prototypes. CFD is used across many industries like aerospace, automotive, biomedical, and more. It complements experimental testing by reducing costs and providing comprehensive flow field data. The document discusses the basics of CFD including discretization methods like finite difference and finite volume, common boundary conditions, and where CFD is applied.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. CFD uses three-dimensional simulations of fluid flow by solving the Navier-Stokes equations with computational algorithms and systems. It gives a comprehensive flow field view not possible through experimental testing alone. CFD has advantages of low cost, speed, ability to simulate real and ideal conditions, and providing comprehensive flow parameter information. Limitations include reliance on accurate physical models, presence of numerical errors, and accuracy of boundary conditions provided. CFD has applications in aerospace, automotive, HVAC, bio-medical, and other industries. Commercial CFD software packages are available
This document provides an overview of computational fluid dynamics (CFD) modeling and simulation using commercial CFD software. It discusses the key steps in the CFD process including defining the geometry, governing equations, boundary conditions, meshing, solving the equations numerically, and post-processing the results. Examples of applications in aerospace, automotive, and other industries are given. The document also summarizes some of the main features and capabilities of the Fluent CFD software.
This document discusses using computational fluid dynamics (CFD) to analyze the flow through a gear pump. It provides background on CFD methodology and applications. It then describes the specific problem of simulating flow through an external gear pump using ANSYS Fluent. It details the geometry, mesh, boundary conditions, solver settings and dynamic mesh setup used. The goal is to determine the mass flow rate of oil through the pump.
The document discusses concepts of computational fluid dynamics (CFD) including:
- CFD is entering a new phase with emphasis on product development and optimization and wider applications. Industrial CFD codes have attributes required for quick turnaround like fast meshing and solvers.
- Improvements are needed in key areas like better accuracy and wider multiphysics capability.
- CFD is used to analyze problems involving fluid flow, heat transfer, mass transfer, chemical reactions, combustion, and multiphase flow.
- CFD involves computer-based simulation of fluid flow, heat transfer, and associated phenomena like chemical reactions.
This document provides an overview of a Computational Fluid Dynamics (CFD) training course held from May 22-27, 2017 in Mumbai, India. The course will cover the basics of CFD including definitions, how CFD can help with design, the analysis process and steps, governing equations, input requirements, boundary and initial conditions, turbulence modeling, and numerical solution methods. The instructor has over 15 years of experience in hydraulic design engineering and will ensure attendees have a strong understanding of theoretical fluid dynamics and heat transfer needed to properly apply and interpret CFD simulations.
This document discusses practical considerations for computational fluid dynamics (CFD) modeling. It addresses important flow physics, geometry simplifications, boundary definitions, mesh quality, wall functions, convergence criteria, sources of error and uncertainty, and the importance of verification and validation. Key points covered include resolving important flow features, conducting a grid independence study, monitoring convergence, and quantifying errors and uncertainties to obtain accurate CFD results.
Transonic turbulent flow around an aerofoil using cfdSukanto Bagchi
Aerofoils are two-dimensional cross-sections of wings that generate lift to balance aircraft. Hydrofoils are underwater wings that allow boats to "fly" on water. Computational fluid dynamics (CFD) uses computer simulations to analyze fluid flow, heat transfer, and other phenomena by solving equations governing fluid motion. CFD was used to study the effects of angle of attack, Reynolds number, and proximity to walls on conventional and non-conventional hydrofoil sections. Results showed thicker hydrofoils perform better at large angles of attack while thinner foils are better for applications requiring small angles of attack like hydrofoil crafts.
July 8th 2014 - Presentation by Mario Caponnetto: "CFD method for foil design"Foiling Week™
1) CFD methods have advanced to the point where they can provide results equivalent to wind tunnel and towing tank tests for most standard naval architecture computations.
2) Early CFD methods like panel and lifting surface methods provided simplified approximations that captured basic aerodynamic behavior but were limited by their neglect of viscosity.
3) Modern VOF solvers can model complex free surface phenomena like spray, waves, cavitation, and ventilation that are important for high-speed marine foils.
This document provides an overview of computational fluid dynamics (CFD) and the CFD analysis process. It discusses:
- What CFD is and how it helps with design by allowing engineers to simulate fluid flow and heat transfer.
- The typical steps in a CFD analysis, including defining the problem, preprocessing like meshing, solving the equations, and postprocessing the results.
- The governing equations that are solved in CFD, including conservation of mass, momentum, and energy.
- The inputs required from users like material properties, boundary conditions, initial conditions, and turbulence models.
- Key aspects of setting up the problem like selecting appropriate boundary conditions, initial conditions, and turbulence modeling
CFD simulation results are only as accurate as the underlying physics models and the operator's skills. Appropriate boundary conditions and a good understanding of the numerical solution algorithms are crucial for accurate results. While CFD is a powerful tool, it is not a substitute for experimental validation. To validate CFD simulations requires experimental data of similar scope for comparison.
This document provides an overview of computational fluid dynamics (CFD) and the CFD process. CFD involves using computers to simulate fluid flow problems by solving partial differential equations describing conservation laws. The CFD process consists of three main steps: pre-processing to define the problem and mesh; solving using a numerical method; and post-processing to analyze results. Key aspects that must be planned include the problem objectives, domain representation, physical models, and verification of results. Sources of error and uncertainty must also be considered.
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.
Experimental and analytical techniques have limitations in fluid mechanics applications. Computational fluid dynamics (CFD) uses numerical methods like finite difference, finite element, and boundary element to solve the governing equations at discrete points within a domain. It allows for complex simulations that would be difficult or expensive with physical experiments. CFD involves discretizing the domain with grids, solving the equations numerically, and analyzing the results to obtain approximate solutions for fluid flow problems.
This document discusses experimental and analytical techniques in fluid mechanics, as well as computational fluid dynamics (CFD). It notes that full-scale experiments can be difficult or expensive, so analytical models using differential equations are commonly used, though assumptions limit their applicability. CFD solves these equations numerically on a grid using techniques like finite difference, finite element, and boundary element methods. It has applications in automotive and biomedical fields.
This document provides an introduction and overview of computational fluid dynamics (CFD) and the course "Introduction to Computational Fluid Dynamics". The key points covered are:
- The course covers numerical methods in CFD, including discretization techniques, accuracy, stability, grids, boundary conditions, and modeling turbulent flow.
- The learning objectives are for students to understand the role of computation in fluid dynamics and gain practical knowledge in setting up and analyzing simple aerodynamic problems using CFD.
- The course contents include introduction to partial differential equations, finite difference methods, grids, the Euler and Navier-Stokes equations, and case studies of best practices in CFD applications. Hands-on lab sessions make up
Computational fluid dynamics (CFD) is a powerful tool to simulate, analyze, and optimize designs. The leading CFD providers will discuss software features and functionality such as flow features and benefits, solver technology, as well as describe an example of CFD use in the real world.
This document discusses best practices for conducting and reporting on computational fluid dynamics (CFD) analyses to achieve credible and confident results. It emphasizes the importance of verification and validation to demonstrate acceptable levels of error and uncertainty. It provides guidance on quantifying various sources of error in CFD simulations and outlines recommended steps for grid convergence studies, reporting results, and validating simulations against experimental data.
This document provides an introduction to computational fluid dynamics (CFD). It outlines what CFD is, why it is used, where it is applied, and the underlying physics, modeling, numerics, and process involved. CFD uses computer simulations to model and predict fluid flow phenomena by solving partial differential equations that describe fluid motion. It allows for simulation-based design and analysis of fluid dynamics problems that are difficult or impossible to study experimentally. CFD has applications across many industries including aerospace, automotive, biomedical, and power generation. Common models include the Navier-Stokes equations and turbulence models like k-epsilon that account for viscosity and other fluid properties.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. CFD uses three-dimensional simulations of fluid flow by solving the Navier-Stokes equations with computational algorithms and systems. It gives a comprehensive flow field view not possible through experimental testing alone. CFD has advantages of low cost, speed, ability to simulate real and ideal conditions, and providing comprehensive flow parameter information. Limitations include reliance on accurate physical models, presence of numerical errors, and accuracy of boundary conditions provided. CFD has applications in aerospace, automotive, HVAC, bio-medical, and other industries. Commercial CFD software packages are available
This document provides an overview of computational fluid dynamics (CFD) modeling and simulation using commercial CFD software. It discusses the key steps in the CFD process including defining the geometry, governing equations, boundary conditions, meshing, solving the equations numerically, and post-processing the results. Examples of applications in aerospace, automotive, and other industries are given. The document also summarizes some of the main features and capabilities of the Fluent CFD software.
This document discusses using computational fluid dynamics (CFD) to analyze the flow through a gear pump. It provides background on CFD methodology and applications. It then describes the specific problem of simulating flow through an external gear pump using ANSYS Fluent. It details the geometry, mesh, boundary conditions, solver settings and dynamic mesh setup used. The goal is to determine the mass flow rate of oil through the pump.
The document discusses concepts of computational fluid dynamics (CFD) including:
- CFD is entering a new phase with emphasis on product development and optimization and wider applications. Industrial CFD codes have attributes required for quick turnaround like fast meshing and solvers.
- Improvements are needed in key areas like better accuracy and wider multiphysics capability.
- CFD is used to analyze problems involving fluid flow, heat transfer, mass transfer, chemical reactions, combustion, and multiphase flow.
- CFD involves computer-based simulation of fluid flow, heat transfer, and associated phenomena like chemical reactions.
This document provides an overview of a Computational Fluid Dynamics (CFD) training course held from May 22-27, 2017 in Mumbai, India. The course will cover the basics of CFD including definitions, how CFD can help with design, the analysis process and steps, governing equations, input requirements, boundary and initial conditions, turbulence modeling, and numerical solution methods. The instructor has over 15 years of experience in hydraulic design engineering and will ensure attendees have a strong understanding of theoretical fluid dynamics and heat transfer needed to properly apply and interpret CFD simulations.
This document discusses practical considerations for computational fluid dynamics (CFD) modeling. It addresses important flow physics, geometry simplifications, boundary definitions, mesh quality, wall functions, convergence criteria, sources of error and uncertainty, and the importance of verification and validation. Key points covered include resolving important flow features, conducting a grid independence study, monitoring convergence, and quantifying errors and uncertainties to obtain accurate CFD results.
Transonic turbulent flow around an aerofoil using cfdSukanto Bagchi
Aerofoils are two-dimensional cross-sections of wings that generate lift to balance aircraft. Hydrofoils are underwater wings that allow boats to "fly" on water. Computational fluid dynamics (CFD) uses computer simulations to analyze fluid flow, heat transfer, and other phenomena by solving equations governing fluid motion. CFD was used to study the effects of angle of attack, Reynolds number, and proximity to walls on conventional and non-conventional hydrofoil sections. Results showed thicker hydrofoils perform better at large angles of attack while thinner foils are better for applications requiring small angles of attack like hydrofoil crafts.
July 8th 2014 - Presentation by Mario Caponnetto: "CFD method for foil design"Foiling Week™
1) CFD methods have advanced to the point where they can provide results equivalent to wind tunnel and towing tank tests for most standard naval architecture computations.
2) Early CFD methods like panel and lifting surface methods provided simplified approximations that captured basic aerodynamic behavior but were limited by their neglect of viscosity.
3) Modern VOF solvers can model complex free surface phenomena like spray, waves, cavitation, and ventilation that are important for high-speed marine foils.
This document provides an overview of computational fluid dynamics (CFD) and the CFD analysis process. It discusses:
- What CFD is and how it helps with design by allowing engineers to simulate fluid flow and heat transfer.
- The typical steps in a CFD analysis, including defining the problem, preprocessing like meshing, solving the equations, and postprocessing the results.
- The governing equations that are solved in CFD, including conservation of mass, momentum, and energy.
- The inputs required from users like material properties, boundary conditions, initial conditions, and turbulence models.
- Key aspects of setting up the problem like selecting appropriate boundary conditions, initial conditions, and turbulence modeling
CFD simulation results are only as accurate as the underlying physics models and the operator's skills. Appropriate boundary conditions and a good understanding of the numerical solution algorithms are crucial for accurate results. While CFD is a powerful tool, it is not a substitute for experimental validation. To validate CFD simulations requires experimental data of similar scope for comparison.
This document provides an overview of computational fluid dynamics (CFD) and the CFD process. CFD involves using computers to simulate fluid flow problems by solving partial differential equations describing conservation laws. The CFD process consists of three main steps: pre-processing to define the problem and mesh; solving using a numerical method; and post-processing to analyze results. Key aspects that must be planned include the problem objectives, domain representation, physical models, and verification of results. Sources of error and uncertainty must also be considered.
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.
Experimental and analytical techniques have limitations in fluid mechanics applications. Computational fluid dynamics (CFD) uses numerical methods like finite difference, finite element, and boundary element to solve the governing equations at discrete points within a domain. It allows for complex simulations that would be difficult or expensive with physical experiments. CFD involves discretizing the domain with grids, solving the equations numerically, and analyzing the results to obtain approximate solutions for fluid flow problems.
This document discusses experimental and analytical techniques in fluid mechanics, as well as computational fluid dynamics (CFD). It notes that full-scale experiments can be difficult or expensive, so analytical models using differential equations are commonly used, though assumptions limit their applicability. CFD solves these equations numerically on a grid using techniques like finite difference, finite element, and boundary element methods. It has applications in automotive and biomedical fields.
This document provides an introduction and overview of computational fluid dynamics (CFD) and the course "Introduction to Computational Fluid Dynamics". The key points covered are:
- The course covers numerical methods in CFD, including discretization techniques, accuracy, stability, grids, boundary conditions, and modeling turbulent flow.
- The learning objectives are for students to understand the role of computation in fluid dynamics and gain practical knowledge in setting up and analyzing simple aerodynamic problems using CFD.
- The course contents include introduction to partial differential equations, finite difference methods, grids, the Euler and Navier-Stokes equations, and case studies of best practices in CFD applications. Hands-on lab sessions make up
Computational fluid dynamics (CFD) is a powerful tool to simulate, analyze, and optimize designs. The leading CFD providers will discuss software features and functionality such as flow features and benefits, solver technology, as well as describe an example of CFD use in the real world.
This document discusses best practices for conducting and reporting on computational fluid dynamics (CFD) analyses to achieve credible and confident results. It emphasizes the importance of verification and validation to demonstrate acceptable levels of error and uncertainty. It provides guidance on quantifying various sources of error in CFD simulations and outlines recommended steps for grid convergence studies, reporting results, and validating simulations against experimental data.
This document provides an introduction to computational fluid dynamics (CFD). It outlines what CFD is, why it is used, where it is applied, and the underlying physics, modeling, numerics, and process involved. CFD uses computer simulations to model and predict fluid flow phenomena by solving partial differential equations that describe fluid motion. It allows for simulation-based design and analysis of fluid dynamics problems that are difficult or impossible to study experimentally. CFD has applications across many industries including aerospace, automotive, biomedical, and power generation. Common models include the Navier-Stokes equations and turbulence models like k-epsilon that account for viscosity and other fluid properties.
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CFD_Lecture_(Introduction_to_CFD).ppt
1. Introduction to Computational
Fluid Dynamics (CFD)
Tao Xing, Shanti Bhushan and Fred Stern
IIHR—Hydroscience & Engineering
C. Maxwell Stanley Hydraulics Laboratory
The University of Iowa
57:020 Mechanics of Fluids and Transport Processes
http://css.engineering.uiowa.edu/~fluids/
Ocrtober 7, 2009
2. 2
Outline
1. What, why and where of CFD?
2. Modeling
3. Numerical methods
4. Types of CFD codes
5. CFD Educational Interface
6. CFD Process
7. Example of CFD Process
8. 57:020 CFD Labs
3. 3
What is CFD?
• CFD is the simulation of fluids engineering systems using modeling
(mathematical physical problem formulation) and numerical methods
(discretization methods, solvers, numerical parameters, and grid
generations, etc.)
• Historically only Analytical Fluid Dynamics (AFD) and Experimental
Fluid Dynamics (EFD).
• CFD made possible by the advent of digital computer and advancing
with improvements of computer resources
(500 flops, 194720 teraflops, 2003 1.3 pentaflops, Roadrunner at
Las Alamos National Lab, 2009.)
4. 4
Why use CFD?
• Analysis and Design
1. Simulation-based design instead of “build & test”
More cost effective and more rapid than EFD
CFD provides high-fidelity database for diagnosing flow
field
2. Simulation of physical fluid phenomena that are
difficult for experiments
Full scale simulations (e.g., ships and airplanes)
Environmental effects (wind, weather, etc.)
Hazards (e.g., explosions, radiation, pollution)
Physics (e.g., planetary boundary layer, stellar
evolution)
• Knowledge and exploration of flow physics
5. 5
Where is CFD used?
• Where is CFD used?
• Aerospace
• Automotive
• Biomedical
• Chemical
Processing
• HVAC
• Hydraulics
• Marine
• Oil & Gas
• Power Generation
• Sports
F18 Store Separation
Temperature and natural
convection currents in the eye
following laser heating.
Aerospace
Automotive
Biomedical
6. 6
Where is CFD used?
Polymerization reactor vessel - prediction
of flow separation and residence time
effects.
Streamlines for workstation
ventilation
• Where is CFD used?
• Aerospacee
• Automotive
• Biomedical
• Chemical
Processing
• HVAC
• Hydraulics
• Marine
• Oil & Gas
• Power Generation
• Sports
HVAC
Chemical Processing
Hydraulics
7. 7
Where is CFD used?
• Where is CFD used?
• Aerospace
• Automotive
• Biomedical
• Chemical Processing
• HVAC
• Hydraulics
• Marine
• Oil & Gas
• Power Generation
• Sports
Flow of lubricating
mud over drill bit
Flow around cooling
towers
Marine (movie)
Oil & Gas
Sports
Power Generation
8. 8
Modeling
• Modeling is the mathematical physics problem
formulation in terms of a continuous initial
boundary value problem (IBVP)
• IBVP is in the form of Partial Differential
Equations (PDEs) with appropriate boundary
conditions and initial conditions.
• Modeling includes:
1. Geometry and domain
2. Coordinates
3. Governing equations
4. Flow conditions
5. Initial and boundary conditions
6. Selection of models for different applications
9. 9
Modeling (geometry and domain)
• Simple geometries can be easily created by few geometric
parameters (e.g. circular pipe)
• Complex geometries must be created by the partial
differential equations or importing the database of the
geometry(e.g. airfoil) into commercial software
• Domain: size and shape
• Typical approaches
• Geometry approximation
• CAD/CAE integration: use of industry standards such as
Parasolid, ACIS, STEP, or IGES, etc.
• The three coordinates: Cartesian system (x,y,z), cylindrical
system (r, θ, z), and spherical system(r, θ, Φ) should be
appropriately chosen for a better resolution of the geometry
(e.g. cylindrical for circular pipe).
11. 11
Modeling (governing equations)
• Navier-Stokes equations (3D in Cartesian coordinates)
2
2
2
2
2
2
ˆ
z
u
y
u
x
u
x
p
z
u
w
y
u
v
x
u
u
t
u
2
2
2
2
2
2
ˆ
z
v
y
v
x
v
y
p
z
v
w
y
v
v
x
v
u
t
v
0
z
w
y
v
x
u
t
RT
p
L
v p
p
Dt
DR
Dt
R
D
R
2
2
2
)
(
2
3
Convection Piezometric pressure gradient Viscous terms
Local
acceleration
Continuity equation
Equation of state
Rayleigh Equation
2
2
2
2
2
2
ˆ
z
w
y
w
x
w
z
p
z
w
w
y
w
v
x
w
u
t
w
12. 12
Modeling (flow conditions)
• Based on the physics of the fluids phenomena, CFD
can be distinguished into different categories using
different criteria
• Viscous vs. inviscid (Re)
• External flow or internal flow (wall bounded or not)
• Turbulent vs. laminar (Re)
• Incompressible vs. compressible (Ma)
• Single- vs. multi-phase (Ca)
• Thermal/density effects (Pr, g, Gr, Ec)
• Free-surface flow (Fr) and surface tension (We)
• Chemical reactions and combustion (Pe, Da)
• etc…
13. 13
Modeling (initial conditions)
• Initial conditions (ICS, steady/unsteady flows)
• ICs should not affect final results and only
affect convergence path, i.e. number of
iterations (steady) or time steps (unsteady)
need to reach converged solutions.
• More reasonable guess can speed up the
convergence
• For complicated unsteady flow problems,
CFD codes are usually run in the steady
mode for a few iterations for getting a better
initial conditions
14. 14
Modeling(boundary conditions)
•Boundary conditions: No-slip or slip-free on walls,
periodic, inlet (velocity inlet, mass flow rate, constant
pressure, etc.), outlet (constant pressure, velocity
convective, numerical beach, zero-gradient), and non-
reflecting (for compressible flows, such as acoustics), etc.
No-slip walls: u=0,v=0
v=0, dp/dr=0,du/dr=0
Inlet ,u=c,v=0 Outlet, p=c
Periodic boundary condition in
spanwise direction of an airfoil
o
r
x
Axisymmetric
15. 15
Modeling (selection of models)
• CFD codes typically designed for solving certain fluid
phenomenon by applying different models
• Viscous vs. inviscid (Re)
• Turbulent vs. laminar (Re, Turbulent models)
• Incompressible vs. compressible (Ma, equation of state)
• Single- vs. multi-phase (Ca, cavitation model, two-fluid
model)
• Thermal/density effects and energy equation
(Pr, g, Gr, Ec, conservation of energy)
• Free-surface flow (Fr, level-set & surface tracking model) and
surface tension (We, bubble dynamic model)
• Chemical reactions and combustion (Chemical reaction
model)
• etc…
16. 16
Modeling (Turbulence and free surface models)
• Turbulent models:
• DNS: most accurately solve NS equations, but too expensive
for turbulent flows
• RANS: predict mean flow structures, efficient inside BL but excessive
diffusion in the separated region.
• LES: accurate in separation region and unaffordable for resolving BL
• DES: RANS inside BL, LES in separated regions.
• Free-surface models:
• Surface-tracking method: mesh moving to capture free surface,
limited to small and medium wave slopes
• Single/two phase level-set method: mesh fixed and level-set
function used to capture the gas/liquid interface, capable of
studying steep or breaking waves.
• Turbulent flows at high Re usually involve both large and small scale
vortical structures and very thin turbulent boundary layer (BL) near the wall
17. 17
Examples of modeling (Turbulence and free
surface models)
DES, Re=105, Iso-surface of Q criterion (0.4) for
turbulent flow around NACA12 with angle of attack 60
degrees
URANS, Re=105, contour of vorticity for turbulent
flow around NACA12 with angle of attack 60 degrees
URANS, Wigley Hull pitching and heaving
18. 18
Numerical methods
• The continuous Initial Boundary Value Problems
(IBVPs) are discretized into algebraic equations
using numerical methods. Assemble the system of
algebraic equations and solve the system to get
approximate solutions
• Numerical methods include:
1. Discretization methods
2. Solvers and numerical parameters
3. Grid generation and transformation
4. High Performance Computation (HPC) and post-
processing
19. 19
Discretization methods
• Finite difference methods (straightforward to apply,
usually for regular grid) and finite volumes and finite
element methods (usually for irregular meshes)
• Each type of methods above yields the same solution if
the grid is fine enough. However, some methods are
more suitable to some cases than others
• Finite difference methods for spatial derivatives with
different order of accuracies can be derived using
Taylor expansions, such as 2nd order upwind scheme,
central differences schemes, etc.
• Higher order numerical methods usually predict higher
order of accuracy for CFD, but more likely unstable due
to less numerical dissipation
• Temporal derivatives can be integrated either by the
explicit method (Euler, Runge-Kutta, etc.) or implicit
method (e.g. Beam-Warming method)
20. 20
Discretization methods (Cont’d)
• Explicit methods can be easily applied but yield
conditionally stable Finite Different Equations (FDEs),
which are restricted by the time step; Implicit methods
are unconditionally stable, but need efforts on
efficiency.
• Usually, higher-order temporal discretization is used
when the spatial discretization is also of higher order.
• Stability: A discretization method is said to be stable if
it does not magnify the errors that appear in the course
of numerical solution process.
• Pre-conditioning method is used when the matrix of the
linear algebraic system is ill-posed, such as multi-phase
flows, flows with a broad range of Mach numbers, etc.
• Selection of discretization methods should consider
efficiency, accuracy and special requirements, such as
shock wave tracking.
21. 21
Discretization methods (example)
0
y
v
x
u
2
2
y
u
e
p
x
y
u
v
x
u
u
• 2D incompressible laminar flow boundary layer
m=0
m=1
L-1 L
y
x
m=MM
m=MM+1
(L,m-1)
(L,m)
(L,m+1)
(L-1,m)
1
l
l l
m
m m
u
u
u u u
x x
1
l
l l
m
m m
v
u
v u u
y y
1
l
l l
m
m m
v
u u
y
FD Sign( )<0
l
m
v
l
m
v
BD Sign( )>0
2
1 1
2 2
2
l l l
m m m
u
u u u
y y
2nd order central difference
i.e., theoretical order of accuracy
Pkest= 2.
1st order upwind scheme, i.e., theoretical order of accuracy Pkest= 1
22. 22
Discretization methods (example)
1 1
2 2 2
1
2
1
l l l
l l l l
m m m
m m m m
FD
u v v
y
v u FD u BD u
x y y y y y
BD
y
1
( / )
l
l l
m
m m
u
u p e
x x
B2
B3 B1
B4
1
1 1 2 3 1 4 /
l
l l l l
m m m m m
B u B u B u B u p e
x
1
4 1
1
2 3 1
1 2 3
1 2 3
1 2 1
4
0 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0
l
l
l
l l
mm l
mm
mm
p
B u
B B x e
u
B B B
B B B
B B u p
B u
x e
Solve it using
Thomas algorithm
To be stable, Matrix has to be
Diagonally dominant.
23. 23
Solvers and numerical parameters
• Solvers include: tridiagonal, pentadiagonal solvers,
PETSC solver, solution-adaptive solver, multi-grid
solvers, etc.
• Solvers can be either direct (Cramer’s rule, Gauss
elimination, LU decomposition) or iterative (Jacobi
method, Gauss-Seidel method, SOR method)
• Numerical parameters need to be specified to control
the calculation.
• Under relaxation factor, convergence limit, etc.
• Different numerical schemes
• Monitor residuals (change of results between
iterations)
• Number of iterations for steady flow or number of
time steps for unsteady flow
• Single/double precisions
24. 24
Numerical methods (grid generation)
• Grids can either be structured
(hexahedral) or unstructured
(tetrahedral). Depends upon type of
discretization scheme and application
• Scheme
Finite differences: structured
Finite volume or finite element:
structured or unstructured
• Application
Thin boundary layers best
resolved with highly-stretched
structured grids
Unstructured grids useful for
complex geometries
Unstructured grids permit
automatic adaptive refinement
based on the pressure gradient,
or regions interested (FLUENT)
structured
unstructured
25. 25
Numerical methods (grid
transformation)
y
x
o o
Physical domain Computational domain
x x
f f f f f
x x x
y y
f f f f f
y y y
•Transformation between physical (x,y,z)
and computational (,,z) domains,
important for body-fitted grids. The partial
derivatives at these two domains have the
relationship (2D as an example)
Transform
26. 26
High performance computing
• CFD computations (e.g. 3D unsteady flows) are usually very expensive
which requires parallel high performance supercomputers (e.g. IBM
690) with the use of multi-block technique.
• As required by the multi-block technique, CFD codes need to be
developed using the Massage Passing Interface (MPI) Standard to
transfer data between different blocks.
• Emphasis on improving:
• Strong scalability, main bottleneck pressure Poisson solver for incompressible flow.
• Weak scalability, limited by the memory requirements.
Figure: Strong scalability of total times without I/O for
CFDShip-Iowa V6 and V4 on NAVO Cray XT5 (Einstein) and
IBM P6 (DaVinci) are compared with ideal scaling.
Figure: Weak scalability of total times without I/O for CFDShip-Iowa
V6 and V4 on IBM P6 (DaVinci) and SGI Altix (Hawk) are compared
with ideal scaling.
27. 27
• Post-processing: 1. Visualize the CFD results (contour, velocity
vectors, streamlines, pathlines, streak lines, and iso-surface in
3D, etc.), and 2. CFD UA: verification and validation using EFD
data (more details later)
• Post-processing usually through using commercial software
Post-Processing
Figure: Isosurface of Q=300 colored using piezometric pressure, free=surface colored using z for fully appended Athena,
Fr=0.25, Re=2.9×108. Tecplot360 is used for visualization.
28. 28
Types of CFD codes
• Commercial CFD code: FLUENT, Star-
CD, CFDRC, CFX/AEA, etc.
• Research CFD code: CFDSHIP-IOWA
• Public domain software (PHI3D,
HYDRO, and WinpipeD, etc.)
• Other CFD software includes the Grid
generation software (e.g. Gridgen,
Gambit) and flow visualization software
(e.g. Tecplot, FieldView)
CFDSHIPIOWA
29. 29
CFD Educational Interface
Lab1: Pipe Flow Lab 2: Airfoil Flow Lab3: Diffuser Lab4: Ahmed car
1. Definition of “CFD Process”
2. Boundary conditions
3. Iterative error
4. Grid error
5. Developing length of
laminar and turbulent pipe
flows.
6. Verification using AFD
7. Validation using EFD
1. Boundary conditions
2. Effect of order of accuracy
on verification results
3. Effect of grid generation
topology, “C” and “O”
Meshes
4. Effect of angle of
attack/turbulent models on
flow field
5. Verification and Validation
using EFD
1. Meshing and iterative
convergence
2. Boundary layer
separation
3. Axial velocity profile
4. Streamlines
5. Effect of turbulence
models
6. Effect of expansion
angle and comparison
with LES, EFD, and
RANS.
1. Meshing and iterative
convergence
2. Boundary layer separation
3. Axial velocity profile
4. Streamlines
5. Effect of slant angle and
comparison with LES,
EFD, and RANS.
30. 30
CFD process
• Purposes of CFD codes will be different for different
applications: investigation of bubble-fluid interactions for bubbly
flows, study of wave induced massively separated flows for
free-surface, etc.
• Depend on the specific purpose and flow conditions of the
problem, different CFD codes can be chosen for different
applications (aerospace, marines, combustion, multi-phase
flows, etc.)
• Once purposes and CFD codes chosen, “CFD process” is the
steps to set up the IBVP problem and run the code:
1. Geometry
2. Physics
3. Mesh
4. Solve
5. Reports
6. Post processing
32. 32
Geometry
• Selection of an appropriate coordinate
• Determine the domain size and shape
• Any simplifications needed?
• What kinds of shapes needed to be used to best
resolve the geometry? (lines, circular, ovals, etc.)
• For commercial code, geometry is usually created
using commercial software (either separated from the
commercial code itself, like Gambit, or combined
together, like FlowLab)
• For research code, commercial software (e.g.
Gridgen) is used.
33. 33
Physics
• Flow conditions and fluid properties
1. Flow conditions: inviscid, viscous, laminar,
or
turbulent, etc.
2. Fluid properties: density, viscosity, and
thermal conductivity, etc.
3. Flow conditions and properties usually
presented in dimensional form in industrial
commercial CFD software, whereas in non-
dimensional variables for research codes.
• Selection of models: different models usually
fixed by codes, options for user to choose
• Initial and Boundary Conditions: not fixed
by codes, user needs specify them for different
applications.
34. 34
Mesh
• Meshes should be well designed to resolve
important flow features which are dependent upon
flow condition parameters (e.g., Re), such as the
grid refinement inside the wall boundary layer
• Mesh can be generated by either commercial codes
(Gridgen, Gambit, etc.) or research code (using
algebraic vs. PDE based, conformal mapping, etc.)
• The mesh, together with the boundary conditions
need to be exported from commercial software in a
certain format that can be recognized by the
research CFD code or other commercial CFD
software.
35. 35
Solve
• Setup appropriate numerical parameters
• Choose appropriate Solvers
• Solution procedure (e.g. incompressible flows)
Solve the momentum, pressure Poisson
equations and get flow field quantities, such as
velocity, turbulence intensity, pressure and
integral quantities (lift, drag forces)
36. 36
Reports
• Reports saved the time history of the residuals
of the velocity, pressure and temperature, etc.
• Report the integral quantities, such as total
pressure drop, friction factor (pipe flow), lift
and drag coefficients (airfoil flow), etc.
• XY plots could present the centerline
velocity/pressure distribution, friction factor
distribution (pipe flow), pressure coefficient
distribution (airfoil flow).
• AFD or EFD data can be imported and put on
top of the XY plots for validation
37. 37
Post-processing
• Analysis and visualization
• Calculation of derived variables
Vorticity
Wall shear stress
• Calculation of integral parameters: forces,
moments
• Visualization (usually with commercial
software)
Simple 2D contours
3D contour isosurface plots
Vector plots and streamlines
(streamlines are the lines whose
tangent direction is the same as the
velocity vectors)
Animations
38. 38
Post-processing (Uncertainty Assessment)
• Simulation error: the difference between a simulation result
S and the truth T (objective reality), assumed composed of
additive modeling δSM and numerical δSN errors:
Error: Uncertainty:
• Verification: process for assessing simulation numerical
uncertainties USN and, when conditions permit, estimating the
sign and magnitude Delta δ*
SN of the simulation numerical error
itself and the uncertainties in that error estimate USN
I: Iterative, G : Grid, T: Time step, P: Input parameters
• Validation: process for assessing simulation modeling
uncertainty USM by using benchmark experimental data and,
when conditions permit, estimating the sign and magnitude of
the modeling error δSM itself.
D: EFD Data; UV: Validation Uncertainty
SN
SM
S T
S
2
2
2
SN
SM
S U
U
U
J
j
j
I
P
T
G
I
SN
1
2
2
2
2
2
P
T
G
I
SN U
U
U
U
U
)
( SN
SM
D
S
D
E
2
2
2
SN
D
V U
U
U
V
U
E Validation achieved
39. 39
Post-processing (UA, Verification)
• Convergence studies: Convergence studies require a
minimum of m=3 solutions to evaluate convergence with
respective to input parameters. Consider the solutions
corresponding to fine , medium ,and coarse meshes
1
k
S
2
k
S
3
k
S
(i). Monotonic convergence: 0<Rk<1
(ii). Oscillatory Convergence: Rk<0; | Rk|<1
(iii). Monotonic divergence: Rk>1
(iv). Oscillatory divergence: Rk<0; | Rk|>1
21 2 1
k k k
S S
32 3 2
k k k
S S
21 32
k k k
R
• Grid refinement ratio: uniform ratio of grid spacing between meshes.
1
2
3
1
2
m
m k
k
k
k
k
k
k x
x
x
x
x
x
r
Monotonic Convergence
Monotonic Divergence Oscillatory Convergence
40. 40
Post-processing (Verification, RE)
• Generalized Richardson Extrapolation (RE): For
monotonic convergence, generalized RE is used
to estimate the error δ*
k and order of accuracy pk
due to the selection of the kth input parameter.
• The error is expanded in a power series expansion
with integer powers of xk as a finite sum.
• The accuracy of the estimates depends on how
many terms are retained in the expansion, the
magnitude (importance) of the higher-order terms,
and the validity of the assumptions made in RE
theory
41. 41
Post-processing (Verification, RE)
)
(i
k
p
i
k
p
n
i
k
k g
x
i
k
m
m
1
*
1
21
1
1
*
*
k
k p
k
k
RE
k
r
k
k
k
k
r
p
ln
ln 21
32
J
k
j
j
jm
k
C
I
k
k m
m
k
m
m
S
S
S
,
1
*
*
*
ˆ
J
k
j
j
jm
i
k
p
n
i
k
C
k g
x
S
S
i
k
m
m
,
1
*
)
(
1
)
(
ˆ
Power series expansion
Finite sum for the kth
parameter and mth solution
order of accuracy for the ith term
Three equations with three unknowns
J
k
j
j
j
k
p
k
C
k g
x
S
S k
,
1
*
1
)
1
(
)
1
(
1
1
ˆ
J
k
j
j
j
k
p
k
k
C
k g
x
r
S
S k
,
1
*
3
)
1
(
2
)
1
(
1
3
ˆ
J
k
j
j
j
k
p
k
k
C
k g
x
r
S
S k
,
1
*
2
)
1
(
)
1
(
1
2
ˆ
SN
SN
SN
*
*
SN
C S
S
εSN is the error in the estimate
SC is the numerical benchmark
42. 42
Post-processing (UA, Verification, cont’d)
• Monotonic Convergence: Generalized Richardson
Extrapolation
*
1
2
*
1
1
.
0
1
4
.
2
1
1
k
RE
k
k
RE
k
C
C
kc
U
• Oscillatory Convergence: Uncertainties can be estimated, but without
signs and magnitudes of the errors.
• Divergence
L
U
k S
S
U
2
1
1. Correction
factors
2. GCI approach *
1
k
RE
s
k F
U
*
1
1 k
RE
s
kc F
U
32 21
ln
ln
k k
k
k
p
r
1
1
k
kest
p
k
k p
k
r
C
r
1
* 21
1
k k
k
RE p
k
r
1
1
2 *
*
9.6 1 1.1
2 1 1
k
k
k RE
k
k RE
C
U
C
1 0.125
k
C
1 0.125
k
C
1 0.25
k
C
25
.
0
|
1
|
k
C
|
|
|]
1
[| *
1
k
RE
k
C
• In this course, only grid uncertainties studied. So, all the variables with
subscribe symbol k will be replaced by g, such as “Uk” will be “Ug”
est
k
p is the theoretical order of accuracy, 2 for 2nd
order and 1 for 1st order schemes k
U is the uncertainties based on fine mesh
solution, is the uncertainties based on
numerical benchmark SC
kc
U
is the correction factor
k
C
FS: Factor of Safety
43. 43
• Asymptotic Range: For sufficiently small xk, the
solutions are in the asymptotic range such that
higher-order terms are negligible and the
assumption that and are independent of xk
is valid.
• When Asymptotic Range reached, will be close to
the theoretical value , and the correction factor
will be close to 1.
• To achieve the asymptotic range for practical
geometry and conditions is usually not possible and
number of grids m>3 is undesirable from a
resources point of view
Post-processing (Verification,
Asymptotic Range)
i
k
p
i
k
g
est
k
p
k
p
k
C
44. 44
Post-processing (UA, Verification, cont’d)
• Verification for velocity profile using AFD: To avoid ill-
defined ratios, L2 norm of the G21 and G32 are used to define RG
and PG
2
2 32
21 G
G
G
R
NOTE: For verification using AFD for axial velocity profile in laminar pipe flow (CFD
Lab1), there is no modeling error, only grid errors. So, the difference between CFD and
AFD, E, can be plot with +Ug and –Ug, and +Ugc and –Ugc to see if solution was
verified.
G
G
G
G
r
p
ln
ln
2
2 21
32
Where <> and || ||2 are used to denote a profile-averaged quantity (with ratio of
solution changes based on L2 norms) and L2 norm, respectively.
45. 45
Post-processing (Verification: Iterative
Convergence)
•Typical CFD solution techniques for obtaining steady state solutions
involve beginning with an initial guess and performing time marching or
iteration until a steady state solution is achieved.
•The number of order magnitude drop and final level of solution residual
can be used to determine stopping criteria for iterative solution techniques
(1) Oscillatory (2) Convergent (3) Mixed oscillatory/convergent
Iteration history for series 60: (a). Solution change (b) magnified view of total
resistance over last two periods of oscillation (Oscillatory iterative convergence)
(b)
(a)
)
(
2
1
L
U
I S
S
U
46. 46
Post-processing (UA, Validation)
V
U
E
E
UV
Validation achieved
Validation not achieved
• Validation procedure: simulation modeling uncertainties
was presented where for successful validation, the comparison
error, E, is less than the validation uncertainty, Uv.
• Interpretation of the results of a validation effort
• Validation example
Example: Grid study
and validation of
wave profile for
series 60
2
2
D
SN
V U
U
U
)
( SN
SM
D
S
D
E
47. 47
Example of CFD Process using CFD
educational interface (Geometry)
• Turbulent flows (Re=143K) around Clarky airfoil with
angle of attack 6 degree is simulated.
• “C” shape domain is applied
• The radius of the domain Rc and downstream length
Lo should be specified in such a way that the
domain size will not affect the simulation results