SlideShare a Scribd company logo

FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS

•Download as PPT, PDF•
•
Aleix Valls
Aleix Valls
1 of 23
FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS Aleix Valls Tomas International Center for Numerical Methods in Engineering (CIMNE) Modulo C1. Despacho C2. Universidad Politécnica de Cataluña. Campus Norte UPC, 08034 Barcelona, Spain [email_address]
Introduction ,[object Object],[object Object],Numerical Oscillations FIC Stabilization
[object Object],[object Object],[object Object],FIC Governing equations d 2 d d 1 A C B q A q B
FIC Governing equations ,[object Object],= FIC
FIC Governing equations ,[object Object],[object Object],[object Object],[object Object],[object Object],FIC Stabilization terms
Finite element discretization ,[object Object],[object Object],[object Object],[object Object]
Finite element discretization ,[object Object],[object Object]
Finite element discretization ,[object Object],[object Object],[object Object],[object Object]
Computation of the characteristic length vector ,[object Object],[object Object],[object Object]
Computation of the characteristic length vector ,[object Object],[object Object]
Computation of the characteristic length vector ,[object Object],[object Object]
Computation of the characteristic length vector ,[object Object],[object Object],[object Object]
Computation of the characteristic length vector ,[object Object],[object Object],[object Object]
Orthotropic Matrix Diffusion ,[object Object],FIC governing equations introduce orthotropic diffusion matrix
About the FIC method ,[object Object],[object Object],[object Object]
About the FIC method ,[object Object],[object Object]
General iterative scheme ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Examples ,[object Object]
Example 1 SUPG FIC
Example 1 Cut y=0.5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 X Phi SUPG FIC
Example 2
Example 2 SUPG FIC
Example 2

Recommended

Choice of weighting function and expansion function in cem
Choice of weighting function and expansion function in cemChoice of weighting function and expansion function in cem
Choice of weighting function and expansion function in cemMohit Chimankar
 
Split result 2021_05_07_10_11_44
Split result 2021_05_07_10_11_44Split result 2021_05_07_10_11_44
Split result 2021_05_07_10_11_44Reema
 
Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Hattori Sidek
 
A technique to construct linear trend free fractional factorial design using...
A technique to construct linear trend free fractional factorial design using...A technique to construct linear trend free fractional factorial design using...
A technique to construct linear trend free fractional factorial design using...Premier Publishers
 
Performance Assessment of Polyphase Sequences Using Cyclic Algorithm
Performance Assessment of Polyphase Sequences Using Cyclic AlgorithmPerformance Assessment of Polyphase Sequences Using Cyclic Algorithm
Performance Assessment of Polyphase Sequences Using Cyclic Algorithmrahulmonikasharma
 
Implimenting_HJM
Implimenting_HJMImplimenting_HJM
Implimenting_HJMAbukar Ali, CQF
 
REDES NEURONALES Performance Optimization
REDES NEURONALES Performance OptimizationREDES NEURONALES Performance Optimization
REDES NEURONALES Performance OptimizationESCOM
 
Vector calculus
Vector calculusVector calculus
Vector calculusARJUN RASTOGI
 

Recommended

Choice of weighting function and expansion function in cem
Choice of weighting function and expansion function in cemChoice of weighting function and expansion function in cem
Choice of weighting function and expansion function in cemMohit Chimankar
 
Split result 2021_05_07_10_11_44
Split result 2021_05_07_10_11_44Split result 2021_05_07_10_11_44
Split result 2021_05_07_10_11_44Reema
 
Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Hattori Sidek
 
A technique to construct linear trend free fractional factorial design using...
A technique to construct linear trend free fractional factorial design using...A technique to construct linear trend free fractional factorial design using...
A technique to construct linear trend free fractional factorial design using...Premier Publishers
 
Performance Assessment of Polyphase Sequences Using Cyclic Algorithm
Performance Assessment of Polyphase Sequences Using Cyclic AlgorithmPerformance Assessment of Polyphase Sequences Using Cyclic Algorithm
Performance Assessment of Polyphase Sequences Using Cyclic Algorithmrahulmonikasharma
 
Implimenting_HJM
Implimenting_HJMImplimenting_HJM
Implimenting_HJMAbukar Ali, CQF
 
REDES NEURONALES Performance Optimization
REDES NEURONALES Performance OptimizationREDES NEURONALES Performance Optimization
REDES NEURONALES Performance OptimizationESCOM
 
Vector calculus
Vector calculusVector calculus
Vector calculusARJUN RASTOGI
 
9702 w01 ms_3
9702 w01 ms_39702 w01 ms_3
9702 w01 ms_3ilovestudyingbio
 
Signal Processing Assignment Help
Signal Processing Assignment HelpSignal Processing Assignment Help
Signal Processing Assignment HelpMatlab Assignment Experts
 
Unit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plotUnit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plotPrajakta Pardeshi
 
report
reportreport
reportmurali vnv
 
Dimensional analysis
Dimensional analysisDimensional analysis
Dimensional analysisnishajj
 
Design of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lectureDesign of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lectureKhalaf Gaeid Alshammery
 
Comparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithmsComparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithmsTanvi Prabhu Dessai
 
Ch7 frequency response analysis
Ch7 frequency response analysisCh7 frequency response analysis
Ch7 frequency response analysisElaf A.Saeed
 
control engineering revision
control engineering revisioncontrol engineering revision
control engineering revisionragu nath
 
Cpnm lect 2-4
Cpnm lect 2-4Cpnm lect 2-4
Cpnm lect 2-4SANDIP GHARAT
 
Lec 4 design via frequency response
Lec 4 design via frequency responseLec 4 design via frequency response
Lec 4 design via frequency responseBehzad Farzanegan
 
Ch6 root locus method
Ch6 root locus methodCh6 root locus method
Ch6 root locus methodElaf A.Saeed
 
Stability and pole location
Stability and pole locationStability and pole location
Stability and pole locationssuser5d64bb
 
case study of curve fitting
case study of curve fittingcase study of curve fitting
case study of curve fittingAdarsh Patel
 
Position analysis and dimensional synthesis
Position analysis and dimensional synthesisPosition analysis and dimensional synthesis
Position analysis and dimensional synthesisPreetshah1212
 
Unit 4.pptx cs
Unit 4.pptx csUnit 4.pptx cs
Unit 4.pptx csSurekha PuriGosavi
 
sample pages 3, CFD report
sample pages 3, CFD reportsample pages 3, CFD report
sample pages 3, CFD report"Prithviraj ("Raj"​)" Rao
 
Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1mkazree
 
Bode Plots
Bode Plots Bode Plots
Bode Plots Hussain K
 
Fourier Transform Assignment Help
Fourier Transform Assignment HelpFourier Transform Assignment Help
Fourier Transform Assignment HelpMatlab Assignment Experts
 
A Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdfA Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdfJackie Gold
 
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...IOSR Journals
 

More Related Content

What's hot

Unit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plotUnit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plotPrajakta Pardeshi
 
Dimensional analysis
Dimensional analysisDimensional analysis
Dimensional analysisnishajj
 
Design of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lectureDesign of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lectureKhalaf Gaeid Alshammery
 
Comparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithmsComparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithmsTanvi Prabhu Dessai
 
Ch7 frequency response analysis
Ch7 frequency response analysisCh7 frequency response analysis
Ch7 frequency response analysisElaf A.Saeed
 
control engineering revision
control engineering revisioncontrol engineering revision
control engineering revisionragu nath
 
Lec 4 design via frequency response
Lec 4 design via frequency responseLec 4 design via frequency response
Lec 4 design via frequency responseBehzad Farzanegan
 
Ch6 root locus method
Ch6 root locus methodCh6 root locus method
Ch6 root locus methodElaf A.Saeed
 
Stability and pole location
Stability and pole locationStability and pole location
Stability and pole locationssuser5d64bb
 
case study of curve fitting
case study of curve fittingcase study of curve fitting
case study of curve fittingAdarsh Patel
 
Position analysis and dimensional synthesis
Position analysis and dimensional synthesisPosition analysis and dimensional synthesis
Position analysis and dimensional synthesisPreetshah1212
 
Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1mkazree
 

What's hot (20)

9702 w01 ms_3
9702 w01 ms_39702 w01 ms_3
9702 w01 ms_3
 
Signal Processing Assignment Help
Signal Processing Assignment HelpSignal Processing Assignment Help
Signal Processing Assignment Help
 
Unit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plotUnit 4 frequency response-Bode plot
Unit 4 frequency response-Bode plot
 
report
reportreport
report
 
Dimensional analysis
Dimensional analysisDimensional analysis
Dimensional analysis
 
Design of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lectureDesign of sampled data control systems part 2. 6th lecture
Design of sampled data control systems part 2. 6th lecture
 
Comparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithmsComparative study of graph partitioning algorithms
Comparative study of graph partitioning algorithms
 
Ch7 frequency response analysis
Ch7 frequency response analysisCh7 frequency response analysis
Ch7 frequency response analysis
 
control engineering revision
control engineering revisioncontrol engineering revision
control engineering revision
 
Cpnm lect 2-4
Cpnm lect 2-4Cpnm lect 2-4
Cpnm lect 2-4
 
Lec 4 design via frequency response
Lec 4 design via frequency responseLec 4 design via frequency response
Lec 4 design via frequency response
 
Ch6 root locus method
Ch6 root locus methodCh6 root locus method
Ch6 root locus method
 
Stability and pole location
Stability and pole locationStability and pole location
Stability and pole location
 
case study of curve fitting
case study of curve fittingcase study of curve fitting
case study of curve fitting
 
Position analysis and dimensional synthesis
Position analysis and dimensional synthesisPosition analysis and dimensional synthesis
Position analysis and dimensional synthesis
 
Unit 4.pptx cs
Unit 4.pptx csUnit 4.pptx cs
Unit 4.pptx cs
 
sample pages 3, CFD report
sample pages 3, CFD reportsample pages 3, CFD report
sample pages 3, CFD report
 
Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1Meeting w3 chapter 2 part 1
Meeting w3 chapter 2 part 1
 
Bode Plots
Bode Plots Bode Plots
Bode Plots
 
Fourier Transform Assignment Help
Fourier Transform Assignment HelpFourier Transform Assignment Help
Fourier Transform Assignment Help
 

Similar to FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS

A Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdfA Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdfJackie Gold
 
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...IOSR Journals
 
An Introduction to the Finite Element Method
An Introduction to the Finite Element MethodAn Introduction to the Finite Element Method
An Introduction to the Finite Element MethodMohammad Tawfik
 
Numerical Solution of Diffusion Equation by Finite Difference Method
Numerical Solution of Diffusion Equation by Finite Difference MethodNumerical Solution of Diffusion Equation by Finite Difference Method
Numerical Solution of Diffusion Equation by Finite Difference Methodiosrjce
 
HOME ASSIGNMENT (0).pptx
HOME ASSIGNMENT (0).pptxHOME ASSIGNMENT (0).pptx
HOME ASSIGNMENT (0).pptxSayedulHassan1
 
FEM Lecture.ppt
FEM Lecture.pptFEM Lecture.ppt
FEM Lecture.pptjuzaila
 
Certified global minima
Certified global minimaCertified global minima
Certified global minimassuserfa7e73
 
Research Presentation Spring 2008
Research Presentation Spring 2008Research Presentation Spring 2008
Research Presentation Spring 2008alblumberg21
 
Numerical Solutions of Burgers' Equation Project Report
Numerical Solutions of Burgers' Equation Project ReportNumerical Solutions of Burgers' Equation Project Report
Numerical Solutions of Burgers' Equation Project ReportShikhar Agarwal
 
HOME ASSIGNMENT omar ali.pptx
HOME ASSIGNMENT omar ali.pptxHOME ASSIGNMENT omar ali.pptx
HOME ASSIGNMENT omar ali.pptxSayedulHassan1
 
Multiple Regression.ppt
Multiple Regression.pptMultiple Regression.ppt
Multiple Regression.pptTanyaWadhwani4
 
Preconditioning in Large-scale VDA
Preconditioning in Large-scale VDAPreconditioning in Large-scale VDA
Preconditioning in Large-scale VDAJoseph Parks
 
Chp%3 a10.1007%2f978 3-642-55753-8-3
Chp%3 a10.1007%2f978 3-642-55753-8-3Chp%3 a10.1007%2f978 3-642-55753-8-3
Chp%3 a10.1007%2f978 3-642-55753-8-3Sabina Czyż
 
Numerical methods for 2 d heat transfer
Numerical methods for 2 d heat transferNumerical methods for 2 d heat transfer
Numerical methods for 2 d heat transferArun Sarasan
 

Similar to FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS (20)

A Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdfA Bibliography on the Numerical Solution of Delay Differential Equations.pdf
A Bibliography on the Numerical Solution of Delay Differential Equations.pdf
 
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
Numerical Solutions of Stiff Initial Value Problems Using Modified Extended B...
 
An Introduction to the Finite Element Method
An Introduction to the Finite Element MethodAn Introduction to the Finite Element Method
An Introduction to the Finite Element Method
 
Numerical Solution of Diffusion Equation by Finite Difference Method
Numerical Solution of Diffusion Equation by Finite Difference MethodNumerical Solution of Diffusion Equation by Finite Difference Method
Numerical Solution of Diffusion Equation by Finite Difference Method
 
Mlab i
Mlab iMlab i
Mlab i
 
HOME ASSIGNMENT (0).pptx
HOME ASSIGNMENT (0).pptxHOME ASSIGNMENT (0).pptx
HOME ASSIGNMENT (0).pptx
 
FEM Lecture.ppt
FEM Lecture.pptFEM Lecture.ppt
FEM Lecture.ppt
 
Fem lecture
Fem lectureFem lecture
Fem lecture
 
Certified global minima
Certified global minimaCertified global minima
Certified global minima
 
Research Presentation Spring 2008
Research Presentation Spring 2008Research Presentation Spring 2008
Research Presentation Spring 2008
 
Numerical Solutions of Burgers' Equation Project Report
Numerical Solutions of Burgers' Equation Project ReportNumerical Solutions of Burgers' Equation Project Report
Numerical Solutions of Burgers' Equation Project Report
 
HOME ASSIGNMENT omar ali.pptx
HOME ASSIGNMENT omar ali.pptxHOME ASSIGNMENT omar ali.pptx
HOME ASSIGNMENT omar ali.pptx
 
IEEE APE
IEEE APEIEEE APE
IEEE APE
 
Multiple Regression.ppt
Multiple Regression.pptMultiple Regression.ppt
Multiple Regression.ppt
 
Preconditioning in Large-scale VDA
Preconditioning in Large-scale VDAPreconditioning in Large-scale VDA
Preconditioning in Large-scale VDA
 
Chp%3 a10.1007%2f978 3-642-55753-8-3
Chp%3 a10.1007%2f978 3-642-55753-8-3Chp%3 a10.1007%2f978 3-642-55753-8-3
Chp%3 a10.1007%2f978 3-642-55753-8-3
 
Finite Element Methods
Finite Element MethodsFinite Element Methods
Finite Element Methods
 
RS
RSRS
RS
 
Fem lecture
Fem lectureFem lecture
Fem lecture
 
Numerical methods for 2 d heat transfer
Numerical methods for 2 d heat transferNumerical methods for 2 d heat transfer
Numerical methods for 2 d heat transfer
 

FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS

  • 1. FINITE ELEMENT FORMULATION FOR CONVECTIVE-DIFFUSIVE PROBLEMS WITH SHARP GRADIENTS USING FINITE CALCULUS Aleix Valls Tomas International Center for Numerical Methods in Engineering (CIMNE) Modulo C1. Despacho C2. Universidad Politécnica de Cataluña. Campus Norte UPC, 08034 Barcelona, Spain [email_address]
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 20. Example 1 Cut y=0.5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 X Phi SUPG FIC