HIGH-ORDER DIFFERENTIAL APPROXIMATIONS OF DIFFERENCE SCHEMES OF THE DAVYDOV METHOD

Abstract

This article examines the nonlinear, dissipative, and dispersion properties of a multiparameter class of difference splitting schemes using the large-particle method (Davydov's method) for spatially three-dimensional computational fluid dynamics problems. The authors applied high-order differential approximations using the REDUCE-3 computer algebra system, which automated the labor-intensive process of expanding grid functions into Taylor series. In general, hyperbolic equations for the first and subsequent approximations are obtained, containing matrices of approximate viscosity (biviscosity, triviscosity) and approximate dispersion (bidispersion) at higher spatial derivatives.