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titleOverview

The Square 2D case involves thermal diffusion in a horizontal flow on a unit square domain. The numerical heat flux at the bottom boundary (y=0) is checked with the analytical heat flux to a specified tolerance. All boundaries are set to a thermal condition which is a function of x and y, and the initial condition is set to 1.

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titleTemperature Distribution:

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titleSolver Parameters:
  • Equation Set: Scalar 2D
  • Nonlinear Solver: Newton
  • Basis Type: Hierarchical
  • Initial/Max CFL: 1030
  • Target residual: 10-11
  • Preconditioning:
  • Type: ILU (Left)
  • Reordering: MDF
  • Outer GMRES iterations (# restarts): 20
    • Inner GMRES iterations (# Krylov vectors): 200

Tested Outputs

  • L2 error (compared to an exact solution function)
  • Numerical heat flux on inner bottom boundary (y=0)
  • Exact heat flux error on inner boundary
  • L∞ of the exact heat flux error
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titleFlow Conditions:
  • Horizontal Flow
  • Boundary Condition:
  • Non-dimensional viscosity:

Case Specific Details

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titleCase 1 (Non-AdaptiveILU):
  • Solution Order: 2: 3
  • Target residual: 10-11
  • Preconditioning:
    • Type: ILU (Left)
    • Reordering: MDF
    • Outer GMRES iterations (# restarts): 20
    • Inner GMRES iterations (# Krylov vectors): 200
  • Iterations to solve: 2
  • All outputs Heat flux output tested to a tolerance of 10-12

Job File:
Square_Scalar2d_GMRES_CircleBoundaryLayerILU

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titleCase 1 Jacobi


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titleCase 2 (AdaptiveJacobi):
  • Solution Order = 1
  • Additional tested outputs: Heat flux adjoint residual
  • Adaptation parameters:
    • Adaptation Iterations: 2
    • Adaptation Method: Fixed fraction
    • Output Adapted: Heat flux
    • Anisotropy Method: Hessian
  • : 0
  • Target residual: 10-12
  • Preconditioning:
    • Type: Jacobi (Left)
    • Reordering: MDF
    • Outer GMRES iterations (# restarts): 20
    • Inner GMRES iterations (# Krylov vectors): 200
  • Iterations to solve: 2
  • Heat flux output
  • Iterations to solve on each mesh: 2
  • All outputs tested to a tolerance of 10-1012

Job File:
Square_Scalar2d_CircleBoundaryLayerGMRES_AdaptJacobi

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titleCase 2 ILU:


Case Details

Square_Scalar2d_GMRES_ILU

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