Semianalytic method for solving gas dynamics equations in Euler variables

This paper presents a semi-analytical method for solving a system of equations of gas dynamics in Eulerian coordinates. Since only spatial derivatives are replaced by finite differences, the system of gas dynamic equations is reduced to a system of ordinary differential equations on a spatial grid. An approximate analytical solution of this system of differential equations for a small time-interval is used to describe the dynamics of a gas in the entire required time interval. Verification was carried out on one-dimensional test problems on the decay of an arbitrary discontinuity and the propagation of stationary shock waves of various intensities. To compare one-dimensional problems, the solution of test problems is given by the simple-to-implement basic particle-in-cell method. It is shown that the semi-analytical method has high accuracy of calculations, and is also the most universal method for calculating applied problems.