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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.

• Equation Set: Scalar 2D
• Nonlinear Solver: Newton
• Basis Type: Hierarchical
• Initial/Max CFL: 10³⁰

Tested Outputs

• Numerical heat flux on bottom boundary (y=0)
• Exact heat flux error on inner boundary
  
• L_∞ of the exact heat flux error

• Horizontal Flow
  
• Boundary Condition:
  
• Non-dimensional viscosity:
  

• Solution Order: 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
• Heat flux output tested to a tolerance of 10^-12

Job File:
Square_Scalar2d_GMRES_ILU