Recent developments for the multigrid scheme of the DLR TAU-Code
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1 Chart 1 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Recent developments for the multigrid scheme of the DLR TAU-Code Axel Schwöppe Institute of Aerodynamics and Flow Technology Center of Computer Applications in Aerospace Science and Engineering - C 2 A 2 S 2 E
2 Chart 2 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Content Introduction (repeat) Investigated multigrid components Coarse grid discretization Semi-coarsening Prolongation Order of fine grid turbulence equation Summary and open questions
3 Chart 3 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Difficulties using TAU multigrid Stall of residual after several iteration steps Inaccurate coefficients Default agglomeration does not take account of semi-coarsening or line-coarsening
4 Chart 4 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Difficulties using TAU multigrid Stall of residual after several iteration steps Inaccurate coefficients Default agglomeration does not take account of semi-coarsening or line-coarsening
5 Chart 5 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Difficulties using TAU multigrid Stall of residual after several iteration steps Inaccurate coefficients Default agglomeration does not take account of semi-coarsening or line-coarsening Stefan Langer
6 Chart 6 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Difficulties using TAU multigrid Stall of residual after several iteration steps Inaccurate coefficients Default agglomeration does not take account of semi-coarsening or line-coarsening Full multigrid does not provide a sufficient start solution Some cases need a smaller CFL number and/or more artificial dissipation for multigrid than for singlegrid to converge
7 Chart 7 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Questions Where does the improvement come from? Aggregation = Galerkin projection Line-coarsening Retain fine grid geometry Are there other points for improvement? Coarse grid discretization Order of prolongation
8 Chart 8 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Repeat: Questions Where does the improvement come from? Aggregation = Galerkin projection Line-coarsening Retain fine grid geometry Are there other points for improvement? Coarse grid discretization Order of prolongation Fine grid cells Agglomerated cell 1. Inject coarse grid values to finest grid level 2. Compute fluxes over all edges 3. Coarse grid residual = sum over boundary edges of fused cells Stefan Langer
9 Chart 9 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Test case: 2D Zero Pressure Gradient Flat Plate Turbulence Modeling Resource: 3 finest quadrilateral grids 137x97 273x x385 TAU singlegrid converges on each grid TAU multigrid converges sometimes using adjusted parameter setting dependent on grid level
10 Chart 10 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Investigated multigrid components Implemented/tested Semi-coarsening Fixed first cell layer at wall on coarse meshes Linear interpolation for prolongation Face-Tangent and Edge-Normal discretization of coarse diffusive terms Time step control (linear system of relaxation scheme) Limiting of corrections of main and turbulence updates Pitfalls Inconsistent low Mach number preconditioning for LUSGS SGS relaxation solver can fail in parallel mode
11 Chart 11 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Check of coarse grid discretization again Convective terms Central scheme with 1 st order dissipation 1 st order upwind schemes Viscous terms Averaged gradients without correction Gradient construction Green-Gauss W W ij ij = W = 1 2 ij W ( W + W ) i ij e j ij U j U x ij i e ij Turbulence equations (Fully coupled)
12 Chart 12 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Check of coarse grid discretization again Convective terms Central scheme with 1 st order dissipation 1 st order upwind schemes Viscous terms Averaged gradients without correction Gradient construction Green-Gauss W W ij ij = W = 1 2 ij W ( W + W ) i ij e j ij U j U x ij i e ij Turbulence equations (Fully coupled without sources)
13 Chart 13 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Coarse grid discretization components Test case: flat plate GC viscous fluxes Fine grid GC turb. diffusion Turbulent Sources Coarse grid GC viscous fluxes GC turb. diffusion Solution process stalls converges converges stalls stalls stalls stalls converges stalls stalls converges
14 Chart 14 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Coarse grid discretization components Test case: 2D Zero Pressure Gradient Flat Plate Row 1 Current TAU discretization Row 2 Consistent fine and coarse grid discretization Row 3 Without face gradient correction for fine and coarse grid discretization
15 Chart 15 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Corrected coarse grid discretization Convective terms Central scheme with 1 st order dissipation 1 st order upwind schemes Viscous terms Averaged gradients + face-tangent or edge-normal argumentation Gradient construction Green-Gauss Turbulence equations Fully coupled + sources
16 Chart 16 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Test case: 2D Zero Pressure Gradient Flat Plate Corrected coarse grid discretization Turbulence Modeling Resource: 3 finest quadrilateral grids 137x97 273x x385 TAU multigrid converges using same parameter setting on each grid level
17 Chart 17 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: cell centers of coarse grid cells
18 Chart 18 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: centers of coarse grid cells
19 Chart 19 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: centers of coarse grid cells
20 Chart 20 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: centers of coarse grid cells
21 Chart 21 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: centers of coarse grid cells
22 Chart 22 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Intermediate results Corrected coarse grid discretization Seems to be much more stable Test case flat plate: same parameter setting on each grid level 3D test cases: same CFL-number as for singlegrid can be used Same artificial dissipation levels can be used for single and multigrid Full multigrid provides much better start solution Additional questions Quality of coarse grid gradients (Green Gauss, Least Squares, ) Agglomeration: centers of coarse grid cells
23 Chart 23 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Semi-coarsening of TAU Schematic A type of semi-coarsening for the advancing front algorithm Used in structured grid parts (hexahedrons, prisms) Controlled by parameter s b a already fused free neighbor seeding volume From free neighbors select the neighbor whose facet fulfill: mmm a 0,b 0 s < a 1,b 2
24 Chart 24 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Semi-coarsening of TAU Test case: flat plate Grid level 1 Semi-coarsening off Semi-coarsening 0.5
25 Chart 25 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Semi-coarsening of TAU Test case: flat plate Grid level 2 Semi-coarsening off Semi-coarsening 0.5
26 Chart 26 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Semi-coarsening of TAU Test case: flat plate Grid level 3 Semi-coarsening off Semi-coarsening 0.5
27 Chart 27 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Semi-coarsening of TAU Test case: flat plate Obvious improvement of converges s has influence on thickness of semi-coarsening in boundary layer number of coarse grid cells
28 Chart 28 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Structured grid coarsening of TAU Test case: flat plate Obvious improvement of converges by semi-coarsening s has influence on thickness of semi-coarsening in boundary layer number of coarse grid cells and thus on runtime
29 Chart 29 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Prolongation Test case: flat plate Coarse grid corrections Added to finer grid by injection (constant) Smoothed using an explicit Laplacian type smoother Tested Linear interpolation using triangle interpolation
30 Chart 30 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Order of fine grid turbulence equation Test case: RAE2822 Convective terms of fine grid discretization Main equations : 2 nd order Turbulence equation: 1 st / 2 nd order Convective terms of coarse grid discretization Main equations : 1 st order Turbulence equation: 1 st order
31 Chart 31 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, D test case: NASA trap wing configuration (High Lift Prediction Workshop) Grid Structured coarse mesh (by JAXA) 12 million points Flow field AoA = 13 Ma = 0.2 Re = 4.3e6
32 Chart 32 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, D test case: NASA trap wing configuration (High Lift Prediction Workshop) Grid Structured coarse mesh (by JAXA) 12 million points Flow field AoA = 13 Ma = 0.2 Re = 4.3e6 Singlegrid converges
33 Chart 33 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, D test case: NASA trap wing configuration (High Lift Prediction Workshop) Grid Structured coarse mesh (by JAXA) 12 million points Flow field AoA = 13 Ma = 0.2 Re = 4.3e6 3w stalls
34 Chart 34 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, D test case: NASA trap wing configuration (High Lift Prediction Workshop) Grid Structured coarse mesh (by JAXA) 12 million points Flow field AoA = 13 Ma = 0.2 Re = 4.3e6 Turbulence equation of 2v stalls
35 Chart 35 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Summary Coarse grid discretization Sources of turbulence equation are required Face gradient: Average of gradients requires correction (FT or EN) Agglomeration Some type of semi-coarsening (line-coarsening) is very helpful Prolongation Order of interpolation influences convergence Fine/coarse grid discretization Order of fine grid turbulence equation influences multigrid convergence There are still many open questions
36 Chart 36 > 21st NIA CFD Seminar > Axel Schwöppe Recent development s for the multigrid scheme of the DLR TAU-Code > Apr 11, 2013 Open questions Influence of Retaining fine grid geometry Order of prolongation (3D) Gradients of coarse grid discretization Order of turbulence equations Benefit of Galerkin-Projection Retains fine grid geometry Does not need new location of coarse cell centers Does not support linear interpolation for prolongation Efficiency Cycle strategy Multigrid vs. singlegrid
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