This circle boundary layer case involves a heat source being applied to the inner boundary of a vortex flow around a circular annulus of radius r = [ 1 , 2 ]. The numerical heat flux at the inner boundary is checked with the analytical heat flux at the inner boundary to a specified tolerance. All boundaries are set to a thermal boundary layer condition which is a function of r and θ. The applied heat source on the inner boundary is a function of r and θ, and the initial condition is set to 1.

  • Vortex Flow

  • Boundary Condition:
  • Heat Source:

    where
  • Non-dimensional viscosity: ν = 10-2

Solver 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 boundary
    • Exact heat flux error on inner boundary
      • Qexact =
    • L∞ of the exact heat flux error
  • Picture of Source Boundary

Case Specific Details

  • Solution Order: 2
  • Iterations to solve: 2
  • All outputs tested to a tolerance of 10-12

Job File:
Scalar2d_CircleBoundaryLayer

  • Picture of Mesh and Heat Contour
  • 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
  • Iterations to solve on each mesh: 2
  • All outputs tested to a tolerance of 10-10

Job File:
Scalar2d_CircleBoundaryLayer_Adapt

  • Picture of Adapted Meshes and Heat Contours