Let's test some of the ProjectX solvers for the case of a NACA0012 airfoil in compressible, inviscid flow.

Each test case starts with an initial primal solution (sample x-momentum shown below). After reading the input, the results for various nonlinear solvers and linear preconditioners are then compared with previously obtained data to ensure the solvers function correctly.

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.

• Common flow parameters:
  • Freestream Mach number: M _∞ = 0.5
  • Angle of attack: α = 0 °
  • Total pressure: P_t =
  • Total temperature: T_t =
  • Static temperature:
  • CFL: 10³⁰
• Common solver parameters:
  • Preconditioning:
    • Outer GMRES iterations (no. restarts): 20
    • Inner GMRES iterations (no. Krylov vectors): 200
  • Solution order: 2
  • PSequencing: False

• Nonlinear solver:
  • Newton
• Preconditioner:
  • Block Jacobi (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

• Nonlinear solver:
  • Newton
• Preconditioner:
  • Block Jacobi (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

• Nonlinear solver:
  • Newton
• Preconditioner:
  • Incomplete LU (0) (left)
  • 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

• Nonlinear solver:
  • Newton
• Preconditioner:
  ** ?? Incomplete LU (ILUK)
  • Reordering type: Minimum discarded fill
  • Side: Left
• Serial results:
  • Residual norm converges to 4.??·10^-13^ after 5 iterations
  • Drag coefficient: C_D = .53 counts
  • Lift coefficient: C_L = .96 counts
• Parallel results:
  • Residual norm converges to 4.3545·10^-13^ after 5 iterations
  • Drag coefficient: C_D = .5318 counts
  • Lift coefficient: C_L = .9638 counts

• Nonlinear solver:
  • Newton
• 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

• Nonlinear solver:
  • Lean Jacobi
• 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