[302.044] numerical methods in fluid dynamics 2–d lid...
TRANSCRIPT
![Page 1: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/1.jpg)
[302.044] Numerical Methodsin Fluid Dynamics
2–D Lid-Driven CavityIncompressible Navier–Stokes (icoFoam),PISO Algorithm and Mesh Remapping
Univ. Assist. MSc. Francesco Romanò
December 18th, 2014
![Page 2: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/2.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Outline
1 Incompressible Navier–Stokes
2 Lid–Driven Cavity
3 icoFoamMeshingSolver set-upMesh RefinementSolver Re-initializationPISO Algorithm
[302.044] – Univ. Assist. MSc. Francesco Romanò 2/13
![Page 3: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/3.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Incompressible Navier–Stokes Equations
Incompressible Navier–Stokes Equations
∇ · u = 0
u,t +u · ∇u = −∇p+ ν∆u+BC & IC
u = velocity field;p = relative pressure field divided by ρ;ν = kinematic viscosity.
[302.044] – Univ. Assist. MSc. Francesco Romanò 3/13
![Page 4: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/4.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Incompressible Navier–Stokes Equations
Incompressible Navier–Stokes Equations∇ · u = 0
u,t +u · ∇u = −∇p+ ν∆u+BC & IC
u = velocity field;p = relative pressure field divided by ρ;ν = kinematic viscosity.
[302.044] – Univ. Assist. MSc. Francesco Romanò 3/13
![Page 5: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/5.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Incompressible Navier–Stokes Equations
Incompressible Navier–Stokes Equations∇ · u = 0
u,t +u · ∇u = −∇p+ ν∆u+BC & IC
u = velocity field;p = relative pressure field divided by ρ;ν = kinematic viscosity.
[302.044] – Univ. Assist. MSc. Francesco Romanò 3/13
![Page 6: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/6.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityMathematical Problem
Lid–Driven Cavity Problem
∇ · u = 0
u,t +u · ∇u = −∇p+ ν∆
BC :
left edge: No–Slip → u = 0;
right edge: No–Slip → u = 0;
bottom edge: No–Slip → u = 0;
top edge: No–Slip → u = U i;IC : u = 0 , (p = 0);
u = velocity field;p = relative pressure field divided by ρ;ν = kinematic viscosity.
[302.044] – Univ. Assist. MSc. Francesco Romanò 4/13
![Page 7: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/7.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityMathematical Problem
Lid–Driven Cavity Problem
∇ · u = 0
u,t +u · ∇u = −∇p+ ν∆
BC :
left edge: No–Slip → u = 0;
right edge: No–Slip → u = 0;
bottom edge: No–Slip → u = 0;
top edge: No–Slip → u = U i;IC : u = 0 , (p = 0);
u = velocity field;p = relative pressure field divided by ρ;ν = kinematic viscosity.
[302.044] – Univ. Assist. MSc. Francesco Romanò 4/13
![Page 8: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/8.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver
. icoFoam assumes an incompressible, unsteady flow andignores gravity, but it can be also set as a steady solver;
. Because, in general, an exact solution of the analyzedproblems is not known, it is not possible to analyticallyvalidate the code. That is the case in which experimentaldata can be used as benchmark;
. Another way to “validate” the code is to increase the cellssize showing a consistent decrement of the approximationerror. If the Lax’ theorem is applicable, the discrete solutionconverges to the exact one decreasing the characteristicsize of each element.
[302.044] – Univ. Assist. MSc. Francesco Romanò 5/13
![Page 9: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/9.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver. icoFoam assumes an incompressible, unsteady flow and
ignores gravity, but it can be also set as a steady solver;
. Because, in general, an exact solution of the analyzedproblems is not known, it is not possible to analyticallyvalidate the code. That is the case in which experimentaldata can be used as benchmark;
. Another way to “validate” the code is to increase the cellssize showing a consistent decrement of the approximationerror. If the Lax’ theorem is applicable, the discrete solutionconverges to the exact one decreasing the characteristicsize of each element.
[302.044] – Univ. Assist. MSc. Francesco Romanò 5/13
![Page 10: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/10.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver. icoFoam assumes an incompressible, unsteady flow and
ignores gravity, but it can be also set as a steady solver;
. Because, in general, an exact solution of the analyzedproblems is not known, it is not possible to analyticallyvalidate the code. That is the case in which experimentaldata can be used as benchmark;
. Another way to “validate” the code is to increase the cellssize showing a consistent decrement of the approximationerror. If the Lax’ theorem is applicable, the discrete solutionconverges to the exact one decreasing the characteristicsize of each element.
[302.044] – Univ. Assist. MSc. Francesco Romanò 5/13
![Page 11: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/11.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver. icoFoam assumes an incompressible, unsteady flow and
ignores gravity, but it can be also set as a steady solver;
. Because, in general, an exact solution of the analyzedproblems is not known, it is not possible to analyticallyvalidate the code. That is the case in which experimentaldata can be used as benchmark;
. Another way to “validate” the code is to increase the cellssize showing a consistent decrement of the approximationerror. If the Lax’ theorem is applicable, the discrete solutionconverges to the exact one decreasing the characteristicsize of each element.
[302.044] – Univ. Assist. MSc. Francesco Romanò 5/13
![Page 12: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/12.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing
. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 13: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/13.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 14: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/14.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 15: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/15.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 16: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/16.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 17: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/17.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 18: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/18.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;
◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 19: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/19.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;
◦ visualize it with <problem_folder>$ paraFoam and theWireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 20: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/20.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Meshing. At first, an evenly distributed, orthogonal mesh is used;
. Because the problem to solve is a 2–D case, inblockMeshDict an arbitrary thickness is given in z directionand empty is used for the faces having as normal vector k;
. For a coarse grid set-up, the number of cells will beNx = 20 , Ny = 20 (and Nz = 1);
. Algorithm steps:
◦ create the geometry writing the blockMeshDict file andlocating it in <problem_folder>/constant/polyMesh/;
◦ run the command <problem_folder>$ blockMesh;◦ check the mesh with <problem_folder>$ checkMesh;◦ visualize it with <problem_folder>$ paraFoam and the
Wireframe visualization option.
[302.044] – Univ. Assist. MSc. Francesco Romanò 6/13
![Page 21: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/21.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up
. For an incompressible, viscous flow, considering a laminarregime, the only fluid property to specify is the kinematicviscosity (in transportProperties);
. In writing the controlDict file, the setted ∆t should takeinto account numerical stability limits;
. Because the employed grid is Orthogonal, the flagnNonOrthogonalCorrectors in fvSolution is set to 0;
. Starting from resting, homogeneous flow, homogeneousinitial conditions are stored for p and U in the folder<problem_folder>/0/.
[302.044] – Univ. Assist. MSc. Francesco Romanò 7/13
![Page 22: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/22.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. For an incompressible, viscous flow, considering a laminar
regime, the only fluid property to specify is the kinematicviscosity (in transportProperties);
. In writing the controlDict file, the setted ∆t should takeinto account numerical stability limits;
. Because the employed grid is Orthogonal, the flagnNonOrthogonalCorrectors in fvSolution is set to 0;
. Starting from resting, homogeneous flow, homogeneousinitial conditions are stored for p and U in the folder<problem_folder>/0/.
[302.044] – Univ. Assist. MSc. Francesco Romanò 7/13
![Page 23: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/23.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. For an incompressible, viscous flow, considering a laminar
regime, the only fluid property to specify is the kinematicviscosity (in transportProperties);
. In writing the controlDict file, the setted ∆t should takeinto account numerical stability limits;
. Because the employed grid is Orthogonal, the flagnNonOrthogonalCorrectors in fvSolution is set to 0;
. Starting from resting, homogeneous flow, homogeneousinitial conditions are stored for p and U in the folder<problem_folder>/0/.
[302.044] – Univ. Assist. MSc. Francesco Romanò 7/13
![Page 24: [302.044] Numerical Methods in Fluid Dynamics 2–D Lid ...info.tuwien.ac.at/ViennaOpenFOAMUserGroup/NumOpenFOAM_P03.pdf · Cavity icoFoam Meshing Solverset-up Mesh Refinement SolverRe-initialization](https://reader034.vdocuments.net/reader034/viewer/2022051803/5b0710707f8b9a93418dac91/html5/thumbnails/24.jpg)
IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. For an incompressible, viscous flow, considering a laminar
regime, the only fluid property to specify is the kinematicviscosity (in transportProperties);
. In writing the controlDict file, the setted ∆t should takeinto account numerical stability limits;
. Because the employed grid is Orthogonal, the flagnNonOrthogonalCorrectors in fvSolution is set to 0;
. Starting from resting, homogeneous flow, homogeneousinitial conditions are stored for p and U in the folder<problem_folder>/0/.
[302.044] – Univ. Assist. MSc. Francesco Romanò 7/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. For an incompressible, viscous flow, considering a laminar
regime, the only fluid property to specify is the kinematicviscosity (in transportProperties);
. In writing the controlDict file, the setted ∆t should takeinto account numerical stability limits;
. Because the employed grid is Orthogonal, the flagnNonOrthogonalCorrectors in fvSolution is set to 0;
. Starting from resting, homogeneous flow, homogeneousinitial conditions are stored for p and U in the folder<problem_folder>/0/.
[302.044] – Univ. Assist. MSc. Francesco Romanò 7/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up
. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;◦ set time step and data saving/storing options writing
the controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ set the fluid properties in transportPropertiesfile and locating it in <problem_folder>/constant/;
◦ set the initial conditions writing the p and U files andlocating them in <problem_folder>/0/;
◦ set time step and data saving/storing options writingthe controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;
◦ set the initial conditions writing the p and U files andlocating them in <problem_folder>/0/;
◦ set time step and data saving/storing options writingthe controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;
◦ set time step and data saving/storing options writingthe controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;◦ set time step and data saving/storing options writing
the controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;◦ set time step and data saving/storing options writing
the controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;◦ set time step and data saving/storing options writing
the controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:◦ set the fluid properties in transportProperties
file and locating it in <problem_folder>/constant/;◦ set the initial conditions writing the p and U files and
locating them in <problem_folder>/0/;◦ set time step and data saving/storing options writing
the controlDict file and locating it in<problem_folder>/system/;
◦ set discretization and splitting scheme details writingthe fvSchemes and fvSolution files and locating themin <problem_folder>/system/;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 8/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Case folder structure:
→ <problem_folder>/→ 0/
Up
→ constant/transportProperties→ polyMesh/
blockMeshDict→ system/
controlDictfvSchemesfvSolution
[302.044] – Univ. Assist. MSc. Francesco Romanò 9/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: Mesh Refinement. As second try, because of the solution characteristics, a
better result can be obtained refining the mesh in thefour corners of the cavity;
. To proceed, the blockMeshDict file will consist of fourblocks whose simple grading will be used to cluster thenodes nearby the domain corners:
blocks(
hex (<1st block vertices>) (<Nx Ny Nx>) simpleGrading (2.0 2.0 1.0)hex (<2nd block vertices>) (<Nx Ny Nx>) simpleGrading (0.5 2.0 1.0)hex (<3rd block vertices>) (<Nx Ny Nx>) simpleGrading (2.0 0.5 1.0)hex (<4th block vertices>) (<Nx Ny Nx>) simpleGrading (0.5 0.5 1.0)
);
[302.044] – Univ. Assist. MSc. Francesco Romanò 10/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver re-initialization. The set-up used for the solver in the case of a uniform mesh
can be kept unchanged;
. The only necessary changing is in writing the controlDictfile. The selected ∆t should take into account numericalstability limits relative to the new mesh;
. As initial condition, the solution of the previous simulationcan be used mapping it on the current grid:
mapFields <folder to map from> -consistent
. As initial time, the final one of the prevoius solution is set.
[302.044] – Univ. Assist. MSc. Francesco Romanò 11/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up
. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;
◦ create the new mesh with the command<problem_folder>/blockMesh;
◦ map the results on the new grid with the command<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;
◦ map the results on the new grid with the command<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: solver set-up. Algorithm steps:
◦ copy the previous results in an old problem folder:<problem_folder_Old>;
◦ set the new blockMeshDict and controlDict;◦ create the new mesh with the command
<problem_folder>/blockMesh;◦ map the results on the new grid with the command
<problem_folder>/mapFields..<problem_folder_Old> -consistent;
◦ run the icoFoam solver with the command<problem_folder>$ icoFoam;
◦ visualize the results with the command<problem_folder>$ paraFoam.
[302.044] – Univ. Assist. MSc. Francesco Romanò 12/13
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IncompressibleNavier–Stokes
Lid–DrivenCavity
icoFoamMeshingSolver set-upMeshRefinementSolver Re-initializationPISOAlgorithm
Lid–Driven CavityOpenFOAM icoFoam solver
OpenFOAM icoFoam solver: PISO algorithm
[302.044] – Univ. Assist. MSc. Francesco Romanò 13/13