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titleOverview

The 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 ]. This regression test checks the The numerical heat flux at the inner boundary to is checked with the analytical heat flux with at the inner boundary to a specified tolerance. The boundary is 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.
The , and the initial condition is set to 1.

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titleGeneral Case Information:
  • Flow parameters:
    • Vortex Flow
      • Vx = V∞ sin(θ)
      • Vy = V∞ cos(θ)
    • Boundary Condition

where µ is the viscosity, R=1, and c=0.59 (to mimic real boundary layer)

    • Heat source on inner radius boundary
      • S(r,θ)
    • Non-dimensional viscosity: 10-2
  • Solver parameters:
    • Equation Set: Scalar 2D
    • Nonlinear Solver: Newton
    • Basis Type: Hierarchical
    • 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
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titleBoundary conditions:
  • Picture of Source Boundary

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