Comparison of Computational Methods and Approaches Applied in Formulation of Boundary Conditions in Lagrange’s Ballistic Problem

Abstract

This paper compares algorithms for constructing a differential solution to the gas dynamics equations in the surrounding of a moving boundary. In order to compare the algorithms, the Lagrange problem, also known as the piston problem, was chosen as a test problem. A comparison was made between the author’s algorithm based on the method of characteristics and the classical approach with a fictitious cell using the solution of the Riemann problem. Calculations were carried out for the case of subsonic and supersonic gas motion. Comparisons were made on a fixed grid with a dynamically expanding cell (Euler grid) and on a uniformly expanding grid (Arbitrary Lagrangian-Eulerian – ALE grid). The problem was solved using numerical schemes of second order in time and space Lax - Wendroff type: the Richtmyer scheme and the MacCormack scheme. The results of calculations using the characteristics method were used as a benchmark solution. The comparative analysis carried out allows conclusions to be drawn regarding the accuracy of the individual approaches, as well as the scope of their applicability.