semi-analytical method, particle-in-cell method, shock wave, decay of an arbitrary discontinuity
Abstract
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.
Author Biographies
Madina Salimzhanovna Zharylkanova, South Ural State University, Chelyabinsk
Student
Nataliya Leonidovna Klinacheva, South Ural State University, Chelyabinsk
Cand. Sc. (Physics and Mathematics), Associate Professor, Department of “Computational Mechanics”
Aleksandr Pavlovich Yalovets, South Ural State University, Chelyabinsk
Dr. Sc. (Physics and Mathematics), Professor, Department of “Computational Mechanics”
