Complex Conservative Difference Schemes in Modeling of Instabilities and Contact Structures

Abstract

IntroductionThe family of the difference schemes on a minimal stencil is under consideration. Construction of the difference schemes on a minimal stencil is based on the scheme approximation order increasing procedure [1]. This method makes it principally possible to develop the schemes of arbitrary approximation order without extension of the scheme stencil by the use of differential consequences of the initial system of equations. Two-dimensional schemes of similar type for plane and cylinder flow symmetry were presented in [2] - [4]. The schemes on the flow oriented grids for plane, cylinder and spherical flow symmetry supplemented by shock-tracking procedures were presented in [5]. Validation and comparison of calculations with the use of the minimal stencil difference schemes and the other ones was conducted in [5] - [7].