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titleOverview

This circle boundary layer case involves a heat source being applied to 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 is also a function of r and θ, and the initial condition is set to 1.

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titleBoundary conditionsTemperature Distribution:
Picture of Source Boundary

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titleFlow Conditions:
  • Vortex Flow

  • Boundary Condition:
  • Heat Source:

    where
  • Non-dimensional viscosity:
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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 boundary
  • Exact heat flux error on inner boundary
  • L of the exact heat flux error

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titleCase 1 (Non-Adaptive):
  • Solution Order: 2
  • Iterations to solve: 2
  • All outputs tested to a tolerance of 10-12

Job File:
Scalar2d_CircleBoundaryLayer

Temperature Distribution:

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titleCase 1 Mesh

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