A MULTIGRID TVD-TYPE SCHEME FOR COMPUTING INVISCID AND VISCOUS FLOWS

A numerical scheme for the computation of steady-state transonic flow fields is presented, which is based on a total variation diminishing (TVD) approach. Various kinds of the anti-diffusive flux terms have been considered, and their effect on the computed results investigated. The time-dependent governing equations are given in a conservative formulation and solved by a hybrid multistage Runge-Kutta scheme. To obtain an improved convergence rate a multigrid procedure has been added to the scheme. The time-marching method presented has been verified by inviscid and viscous two-dimensional flow-field computations. It has been found that a simple laminar shock-boundary-layer interaction problem serves as a good indicator for the effect of the various flux limiters of a TVD-scheme. On the whole, it has been observed that for the solution of the Euler equations the most diffusive of the limiter functions is capable of yielding a good shock resolution. However, the flux limiters have to be chosen very carefully if viscous flow with separation bubbles is to be considered. The better the shock resolution of the flux limiter applied, the greater the effect the various time-stepping procedures have on the results.