High-Order Workshop Results for Case CR1 RANS of the ...€¦ · High-Order Workshop Results for...
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High-Order Workshop Results for Case CR1 RANS of the Common Research Model (6th AIAA Drag prediction workshop) Michael J. Brazell, Behzad R. Ahrabi, and Dimitri J. Mavriplis Department of Mechanical Engineering University of Wyoming January 6, 2018
Transcript of High-Order Workshop Results for Case CR1 RANS of the ...€¦ · High-Order Workshop Results for...
High-Order Workshop Results for Case CR1RANS of the Common Research Model(6th AIAA Drag prediction workshop)
Michael J. Brazell, Behzad R. Ahrabi, and Dimitri J. Mavriplis
Department of Mechanical EngineeringUniversity of Wyoming
January 6, 2018
Flow Solver
I Discontinuous Galerkin Finite Element Method
I Modal basis functions
I Hybrid mixed element unstructured meshes (tetrahedra,prisms, pyramids, and hexahedra)
I p-enrichment and h-refinement using non-conformingelements (hanging nodes)
I Independent polynomial degree for solution and mapping basis
I Non-linear system solver: PTC Newton-Rhapson method
I Linear system solver: preconditioned flexible-GMRES (Saad1986)
I Line implicit Jacobi, Gauss-Seidel relaxation, ILU(0)
Physics
I Compressible Navier-Stokes in conservative variables
I PDE-based Artificial Viscosity (Barter and Darmofal, Burgess)
I Spalart-Allmaras turbulence model (negative-SA variant)
I Inviscid flux: Lax-Friedrichs, Roe, AUFS
I Viscous flux: symmetric interior penalty (SIP)
Drag and Lift Results
Ma= 0.3, Roe Flux, ILU(0)time/dof = cputime×procs
τ×dofs
case p dof ×106 CL CD time/dof
1 1 7.7 0.39934 .020747 0.153
2 1 9.99 0.39597 .021177 0.098
3 1 19.1 0.39531 .021243 0.048
4 1 42.8 0.39593 .021248 0.101
5 2 19.2 0.39628 .020588 0.202
6 2 249 0.39386 .021104 0.111
7 2 47.7 0.39368 .021164 0.054
8 2 107 0.39372 .021177 0.095
9 3 38.4 0.39542 .020545 0.327
Drag Results
p=1 Laxp=2 Laxp=2 AUFSp=1 Roep=2 Roe -2σp=2 Roe 2σp=2 Roep=3 Roe
10 -31.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.00.0205
0.0206
0.0207
0.0208
0.0209
0.0210
0.0211
0.0212
0.0213
0.0214
0.0215
0.0216
0.0217
0.0218
h = DOF-1/3
CD
Drag Results Zoom
p=1 Laxp=2 Laxp=2 AUFSp=1 Roep=2 Roe -2σp=2 Roe 2σp=2 Roep=3 Roe
10 -31.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.00.0205
0.0206
0.0207
0.0208
0.0209
0.0210
0.0211
0.0212
0.0213
0.0214
0.0215
0.0216
0.0217
0.0218
h = DOF-1/3
CD
p=1 Lax
p=2 Lax
p=2 AUFS
p=1 Roe
p=2 Roe -2σ
p=2 Roe 2σ
p=2 Roe
p=3 Roe0.0021 0.0022
0.02118
0.0212
0.02122
0.02124
0.02126
0.02128
Lift Results
p=1 Laxp=2 Laxp=2 AUFSp=1 Roep=2 Roe -2σp=2 Roe 2σp=2 Roep=3 Roe
10 -31.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.00.393
0.394
0.395
0.396
0.397
0.398
0.399
0.400
0.401
0.402
h = DOF-1/3
CL
Lift Results Zoom
p=1 Laxp=2 Laxp=2 AUFSp=1 Roep=2 Roe -2σp=2 Roe 2σp=2 Roep=3 Roe
10 -31.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.00.393
0.394
0.395
0.396
0.397
0.398
0.399
0.400
0.401
0.402
h = DOF-1/3
CL
p=1 Lax
p=2 Lax
p=2 AUFS
p=1 Roe
p=2 Roe -2σ
p=2 Roe 2σ
p=2 Roe
p=3 Roe
0.0018 0.002 0.0022 0.0024 0.0026
0.394
0.3945
0.395
0.3955
0.396
Residual, tiny mesh, Ma = 0.3
DG3D, CRM, Ma = 0.3, ILU(0), tiny tetrahedral mesh
Krylov vectorsCFLTotal Residual(μt/μref)max
Tota
l Res
idua
l (R
MS)
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
1
CFL
1
101
102
103
104
105
106
Krylov Vectors
1
101
102
103
104
Max μ
t /μo
0
1000
2000
3000
4000
5000
6000
7000
8000
Non-Linear Iterations0 50 100 150 200 250 300 350 400 450 500
Residual, fine mesh, Ma = 0.3
DG3D, CRM, Ma = 0.3, ILU(0), fine tetrahedral mesh
Krylov vectorsCFLTotal Residual(μt/μref)max
Tota
l Res
idua
l (R
MS)
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
1
CFL
1
101
102
103
104
105
106
Krylov Vectors
101
102
103
104
Max μ
t /μo
0
500
1000
1500
2000
2500
3000
Non-Linear Iterations0 50 100 150 200 250 300 350
Res., coarse mesh, Ma = 0.85
CFLResidual
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
10 -5
10 -4
10 -3
10 -2
10 -1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 -5
10 -4
10 -3
10 -2
10 -1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
Non-Linear Iterations
Non
-Lin
ear R
esid
ual,
CFL
p=1Ma=0.5
Ma=0.6
Ma=0.7 Ma=0.75
Ma=0.8
Ma=0.85
p=2Ma=0.85
Pressure contours
Ma = 0.85, P2Q2
Temperature contours
Ma = 0.85, P2Q2
Density contours
Ma = 0.85, P2Q2
Density contours
Ma = 0.85, P2Q2
Density contours
Ma = 0.85, P2Q2
Conclusions
I Converging to a different drag value than other FE codes
I Face fluxes caused larger variation than expected
I Once p=1 is converged rapid convergence is observed forp=2,3
I Transonic case was very difficulty to initialize and requiredmach ramping
I p=1 tetrahedral meshes are painful for DG
I If meshing goes in direction of pure tetrahedral need todevelop cell-based lines that do not rely on prisms
I ILU(0) requires a lot of memory, lines will help with this butalso need matrix free high-order preconditioners
