Steady 2-D advection-diffusion with phi-dependent coefficients

The main program sets up geometry of solution domain for 2-D advective diffusion with uniform density rho. Conductivity Gamma is now a function of phi, and the solution is achieved iteratively.

  • The boundaries of this solution domain are on finite-volume faces, but additional nodes are added on the boundaries (Patankar's Practice B, p.69).
  • Boundary conditions can be either fixed phi or fixed phi gradient at each face on the boundary. For example, in bc_e, first column is numerical value of BC, second column specifies BC type - 1 for value, 2 for gradient. A value of -2 indicates a specified diffusive flux,rather than a phi gradient (that's because Gamma is changing.)
  • Gamma_phi m-file uses 1/phi dependence
  • Gamma_phi_bad m-file uses linear dependence on phi (can get negative Gamma)
  • u.m and w.m find velocities on appropriate volume boundaries
  • A.m and F_upwind.m implement power-law advection scheme

solve.m solves the resulting system of linear equations.

Main Program - SS 2-D Advective Diffusion
Finite-Volume Formulator
Matrix Solver

u velocity
w velocity
Gamma (1/phi)
Gamma (linear with phi)