A multigrid method for the Cauchy-Riemann equations based on flux-difference splitting and its extension to the steady Euler equations

摘要

Flux-vector splitting and flux-difference splitting techniques are applied to the Cauchy-Riemann equations. It is shown that the discrete equations obtained by both techniques can be solved by relaxation methods, which can be used in the multigrid technique. The flux-difference splitting technique is applied to the steady one-dimensional Euler equations and the resulting set of discrete equations is solved by a relaxation algorithm. The solution for transonic flow is free of transition points in the shock region. By analogy with the Cauchy-Riemann equations, it is concluded that] this technique is extendable to two dimensions and that it can be used in the multigrid method.