Stability analysis of schemes with upwind differences for the solution of the system of kinetic equations for the modelling of semi-compressible gas

摘要

Stability analysis of the finite-difference schemes for the solution of the system of kinetic equations is performed. Two types of the schemes are considered: schemes with separate discretization of derivatives in convective terms and schemes with uniform discretization of these terms. Analysis is based on von Neumann method. As a main result of the analysis performed the larger values of the areas of stability domains for the schemes with uniform discretization were obtained. This result allows to recommend this type of numerical schemes for the solution of the hydrodynamical problems for the semi-compressible gases and fluids.