Abstract

The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.

中文翻译：

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Godunov方法的线性化版本的熵性质的研究

摘要

提出了为一维气体动力学方程的双曲系统建立弱解的思想。一个重要的方面是检查实现非递减熵定律的方案，该方案必须适用于弱解，并且从物理学的角度来看是必须的。借助经典Godunov方案的最简单线性化形式，在有限差分公式中定义了弱解的概念。实验表明，该版本可保证熵不变。结果，可以模拟震动波上的熵的增长，而无需使用任何校正项或其他条件。