Numerical simulation of compressible, viscous flow using an implicit, bi-diagonal method

The numerical simulation of compressible viscous flow is investigated with an emphasis on proper boundary conditions for the implicit block bidiagonal method developed by MacCormack (1981). The nature of the predictor-corrector method makes the development of stable implicit boundary conditions difficult. Various boundary conditions were tested on a supersonic diffuser which included shock generation by compression corner, boundary layer shock interaction with separation and reattachment, and termination of shock by expansion corner. A supersonic inflow boundary condition was correct; there were no problems at the supersonic upstream boundary. Solid wall boundary conditions were applied resulting in varying degrees of stability. The type of boundary conditions at the outflow had no influence on the overall convergence and only a limited local effect on the flow variables at the downstream boundary.