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.

中文翻译：

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计算方法与拉格朗日弹道问题边界条件制定方法的比较

本文比较了构建移动边界周围气体动力学方程微分解的算法。为了比较算法，选择拉格朗日问题（也称为活塞问题）作为测试问题。将作者基于特征法的算法与利用黎曼问题求解的虚拟单元的经典方法进行了比较。对亚音速和超音速气体运动情况进行了计算。对具有动态扩展单元（欧拉网格）的固定网格和均匀扩展网格（任意拉格朗日-欧拉 - ALE 网格）进行了比较。该问题使用时空二阶 Lax - Wendroff 型数值格式求解：Richtmyer 格式和 MacCormack 格式。使用特征法的计算结果作为基准解。通过进行比较分析，可以得出有关各个方法的准确性及其适用范围的结论。