# OpenFOAM －空間の離散化と係数行列の取り扱い（Spatial Discretization and Coefficient Matrix）－

May 27, 2015

## Technology

• 1. OpenFOAM Fumiya Nozaki : 2014817 Keywords OpenFOAM

2. 2 (CFD) (discretization) (coefficient matrix) OpenFOAM 3. 3 Chapter 1 Chapter 2 Chapter 3gdbOF Chapter 4 Chapter 5 Chapter 6simpleFoam Chapter 7pUCoupledFoam 4. 4 Chapter 1 5. 5 = 0 + = 1 + NavierStokes , , 100 [1] 6. 6 , , , 1 2 3 4 5 6 , = 6 7. 7 [2] finite difference method : FDM finite volume method : FVM finite element method : FEM 1 2 3 4 5 6 1 1 + 2 2 + 4 4 = 0 8. 8 OpenFOAM OpenFOAM [3] CFD [4] 9. 9 () ( CV ) OpenFOAM CV CV (face) 2 CV CV () f 2 7CV 6CV 10. 10 OpenFOAM 2 = ~ 11. 11 CV 78 OpenFOAM CV + = CV CV OpenFOAMCV CV CVCV 12. CVCV CV 12 1 9 = 1 9 1 2 3 6 5 4 7 8 9 0 CV 13. 13 1 2 3 6 5 4 7 8 9 2CV3CV 2 2 3 2 3 ()2CV ()3CV 14. 14 CV OpenFOAM 15. 15 lduMatrix OpenFOAM diag upper lower lduMatrix upper lower diag 3 16. 16 lduAddressing 3 lduAddressing 2CV lowerAddr upperAddr 7 3CV 5CV 7 = 3 7 = 5 17. 17 -1- -2- -3- -6- -5- -4- -7- -8- -9- 25 = 52 = 33 18. 18 owner neighbour OpenFOAM2(CV) owner neighbour lduAddressing k > k k owner k neighbour 19. 19 fvMatrix source relax residual faceFluxCorrectionPtr flux ( ) internalCoeffs boundaryCoeffs 20. 20 (fixedValue zeroGradient) OpenFOAM4 internalCoeffs boundaryCoeffs - valueInternalCoeffs - valueBoundaryCoeffs gradientInternalCoeffs gradientBoundaryCoeffs CV CV 21. Chapter 2 OpenFOAM 21 22. 22 H.Versteeg, W.Malalasekera An Introduction to Computational Fluid Dynamics: The Finite Volume Method Henk Versteeg http://www.lboro.ac.uk/departments/mechman/staff/henk-versteeg.html W.Malalasekera http://lupo.lboro.ac.uk/staff/malalasekera.html 23. 23 = 0 0.5m A = 100 = 500 B 0 = 100 0.5 = 500 10 103 2 = 1000 1 1 24. 24 = 800 + 100 25. 25 OpenFOAM laplacianFoam 26. laplacianFoam mylaplacianFoam mylaplacianFoam laplacianFoam.C Make files 26 \$ sol \$ cd basic \$ cp r laplacianFoam mylaplacianFoam \$ cd mylaplacianFoam \$ mv laplacianFoam.C mylaplacianFoam.C laplacianFoam.C EXE = \$(FOAM_APPBIN)/laplacianFoam mylaplacianFoam.C EXE = \$(FOAM_USER_APPBIN)/mylaplacianFoam 27. 27 mylaplacianFoam.C #include "fvCFD.H" #include "simpleControl.H" // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // int main(int argc, char *argv[]) { #include "setRootCase.H" #include "createTime.H" #include "createMesh.H" #include "createFields.H" simpleControl simple(mesh); // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // Info

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