First Differential Approximation Method and Approximate Viscosity of Difference Schemes

Abstract

When hyperbolic systems are integrated, effects of so-called approximation viscosity appear. To investigate the latter, there is a very effective method which allows the reduction of the problem of the stability of a difference scheme to the stability (correctness) of a system of differential equations (the so-called first differential approximation). Such a reduction is possible in the classes of simple and majorant schemes. In a sense, the approximation viscosity of the scheme and its dissipative properties are determined by a first differential approximation. The stated method can be used in the investigation of difference schemes for the problems of compressible and viscous fluid.