Flow relaxation method in solving quasilinear parabolic equations

Abstract

This article proposes a numeric method of solution of quasilinear parabolic equations, based on the flux approximation, describes the implementation of the method on a rectangular grid and presents numerical results. Unlike methods used in common practice, this method uses an approximation of flows in non-dilated template. For each iteration of the Newton method it is possible to solve a linear problem using the method of upper relaxation (SOR). Compared with the methods of flux sweeping, the considered method has greater potential for use in modern parallel computing system.

Keywords

• parabolic quasilinear equation
• red-black ordering
• difference scheme
• qasilinearization
• SOR