Page History

Section

Column

width	50%

Panel

title	Background:

...

Let's test some of the ProjectX solvers for the case of a NACA0012

...

Parameters:

airfoil in compressible, inviscid flow.

Each test case starts with an initial primal solution (sample x-momentum shown below). After reading the input, ProjectX runs a particular test case. Subsequently, all numerical data stored in the history (.hist) files are compared with a "true" history file.

In some cases, the solvers are also run in parallel using MPI and compared with the solvers run in serial. The drag and lift coefficients along with residual convergence are given.

For more information, please consult the .job and .hist files located in the corner of each panel.

Column

width	50%

Panel

title	Inputs:

Common flow parameters:
- Equation set: Compressible 2D Euler

Panel

title

- Freestream Mach number: M _∞ = 0.5
- Angle of attack: α = 0 °

Total pressure: P_t; =

Total temperature: T_t; =

Static temperature:

< insert grid image here > < insert primal solution here >

Panel

title	Newton-Jacobi (Right)

what this solver tests
result

Panel

title	Newton-Jacobi

what this solver tests
result

Panel

title	Newton-ILU

what this solver tests
result

- CFL: 10³⁰
Common solver parameters:
- Preconditioning:
  - Outer GMRES iterations (no. restarts): 20
  - Inner GMRES iterations (no. Krylov vectors): 200
- Solution order: 2
- PSequencing: False

Section

Column

width	50%

Panel

title	Boundary conditions:

Image Added

Column

width	50%

Panel

title	Input Primal X-Momentum:

Image Added

...

Linear solver tests:

Section

Column

width	50%

Panel

title	What is being tested?

Listed below are the tolerances for the relevant data compared in the history files:

Solution update fraction: 0.1
Residaul norm: 10^-10
Drag coefficient: 10^-12
Lift coefficient: 10^-12

Column

width	50%

Panel

title	Residual convergence comparison:

Image Added

Section

Column

width	50%

Panel

title	Newton-Jacobi (Left):

Nonlinear solver:
- Newton
Linear solver:
- Proconditioner: Block Jacobi
- Side: Left
Serial results:
- Residual norm converges to 4.3571·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Column

width	50%

Panel

title	Newton-Jacobi (Right):

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner: Block Jacobi
- Side: Right
Results:
- Residual norm converges to 4.3532·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Section

Column

width	50%

Panel

title	Newton-ILU:

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner: Incomplete LU (0)
- Reordering type: Minimum discarded fill
- Side: Left
Serial results:
- Residual norm converges to 4.3566·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts
Parallel results:
- Residual norm converges to 4.3501·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Column

width	50%

Panel

title	Newton-ILUT:

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner:Threshold-based Incomplete LU (ILUT)
- Reordering type: Minimum discarded fill
- Side: Right
- Drop threshold: 10^-3
Serial results:
- Residual norm converges to 4.3538·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts
Parallel results:
- Residual norm converges to 4.3539·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Section

Column

width	50%

Panel

title	Newton-ILU Multigrid:

Nonlinear solver:
- Newton
Linear solver:
- Incomplete LU (0) (left) preconditioner
  - Reordering type: Minimum discarded fill
  - Side: Right
- P = 0 linear multigrid for coarse correction
Serial results:
- Residual norm converges to 3.8091·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts
Parallel results:
- Residual norm converges to 4.3501·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Column

width	50%

Panel

title	Newton-ILU-ASM (with/without multigrid):

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner: Incomplete LU (ILU)
- Parallel preconditioner: Additive Schwarz Method (ASM)
- Side: Right
- Reordering type: Minimum discarded fill
- Outer GMRES iterations: 2
- Inner GMRES iterations: 20
Parallel results (without multigrid):
- Residual norm converges to 4.3736·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts
Parallel results (with multigrid):
- Residual norm converges to 3.8106·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Section

Column

width	50%

Panel

title	Newton-UMFPACK:

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner: Threshold-based Incomplete LU
- Side: Right
- Reordering type: Minimum discarded fill
Serial results:
- Residual norm converges to 4.3559·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts
Parallel results:
- Residual norm converges to 4.3506·10^-13 after 5 iterations
- Drag coefficient: C_D = .5318 counts
- Lift coefficient: C_L = .9638 counts

Column

width	50%

Panel

title	Lean Jacobi:

Nonlinear solver:
- Lean Jacobi
Linear solver:
- Preconditioner: None
Serial results:
- Residual norm converges to 4.7345·10^-4 after 200 iterations
- Drag coefficient: C_D = .5098 counts
- Lift coefficient: C_L = .9478 counts
Parallel results:
- Residual norm converges to 4.7345·10^-4 after 200 iterations
- Drag coefficient: C_D = .5098 counts
- Lift coefficient: C_L = .9478 counts

Section

Column

width	50%

Panel

title	Newton-Osher:

Nonlinear solver:
- Newton
Linear solver:
- Preconditioner: Threshold-based Incomplete LU
- Side: Left
- Reordering type: Minimum discarded fill
Serial results:
- Residual norm converges to 5.6482·10^-14 after 38 iterations
- Drag coefficient: C_D = .5319 counts
- Lift coefficient: C_L = .9653 counts

Column

width	50%

...

Adjoint solver tests:

Section

Column

width	55%

Panel

title	What is being tested?

Listed below are the tolerances for the relevant data compared in the history files:

Adjoint residual: 10^-12

Panel

title	Adjoint solution:

For the primal solution, please refer to the Newton-ILU case above.

Adjoint parameters:
- Adjoint solution computed using drag as output
- Sensitivity parameter: Angle of attack
- Forward sensitivities are computed (i.e. dC_D/dα with a tangent linearization)
Serial results:
- Adjoint residual norm converges to 1.8574·10^-15 after 2 iterations
- dC_D/dα (forward sensitivity): 1.6544·10^-3
- dC_D/dα (adjoint): 1.6544·10^-3

Column

width	45%

Panel

title	Dual X-momentum:

Image Added

...

Adaptation tests:

Section

Column

width	50%

Panel

title	What is being tested?

Listed below are the tolerances for the relevant data compared in the history files:

Number of degrees of freedom on adapted meshes: 1
Error indicator: 10^-12
Error estimate: 10^-12
Drag: 10^-12

Panel

title	Adaptation Test (boundary-curved):

For the primal solution, please refer to the Newton-ILU case above (with Nonlinear solver iterations limited to 50)

Adjoint parameters:
- Adjoint output: Drag
- Patch Reconstruction H1: False
- Hessian Scalar Type: -1
  (Mach number for Hessian evaluation)
- Nonlinear Smoother: Newton (solved to 10^-6)
- Adjoint Smoother residual converged to 10^-6
- Primal truth surrogate not fully converged
- Adjoint truth fully converged
Adaptation parameters:
- Output Adapted: Drag
- Anisotropy method: Hessian
- Curved re-meshing method: Boundary-curved
- Number of adaptation iterations: 2
- hp adaptation space
- Adaptation algorithm: Fixed-Fraction marking
  - 30% refining and 20% coarsening fractions
  - Target degree-of-freedom increase factor: 1.0 (constant DOF)
- Forward sensitivities are computed
  (i.e. dC_D/dα with a tangent linearization)
Serial results:
- Initial mesh:
  - DOF = 990
  - Error estimate = 3.9138·10^-4
  - Drag = 5.3180·10^-4
- First adaptation:
  - DOF = 1008
  - Error estimate = 1.9066·10^-4
  - Drag = 2.6942·10^-4
- Second adaptation:
  - DOF = 1026
  - Error estimate = 1.3617·10^-4
  - Drag = 2.0600·10^-4

Column

width	50%

Panel

title	Adaptation Test (elasticity):

Almost all parameters are identical to the boundary-curved adaptation test. The only differing parameters are:
- Target degree-of-freedom increase factor: 1.25
- Curved re-meshing type: Elasticity
Serial results:
- Initial mesh:
  - DOF = 990
  - Error estimate = 3.9138·10^-4
  - Drag = 5.3180·10^-4
- First adaptation:
  - DOF = 1008
  - Error estimate = 1.8590·10^-4
  - Drag = 2.6109·10^-4
- Second adaptation:
  - DOF = 1278
  - Error estimate = 8.5377·10^-5
  - Drag = 1.3336·10^-4

Panel

title	Primal X-momentum after two adaptation iterations (elasticity):

Image Added

Section

Column

width	50%

Panel

title	Error estimate and drag over two adaptations (boundary-curved):

Image Added

Column

width	50%

Panel

title	Error estimate and drag over two adaptations (elasticity):

Image Added

Panel

title	Newton-ILUT

what this solver tests
result

Child pages

Versions Compared

Old Version 9

New Version Current

Key

Linear solver tests:

Adjoint solver tests:

Adaptation tests: