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The Quartic Poly 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 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.

• 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

• Vortex Flow
  
  
• Boundary Condition:
  
• Heat Source:
  
  where
  
• Non-dimensional viscosity: