论文标题
多变态气体的一维流：谎言组分类，保护法，不变和保守差异方案
One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes
论文作者
论文摘要
本文考虑了三种情况下拉格朗日坐标中多面气体的一维流量：普通的一维流，径向对称的流和球形对称流。 Lagrangian变量中的一个二阶部分微分方程描述了多变态气体的一维流。执行此PDE的谎言组分类。它的变分结构允许借助Noether定理构建保护法。这些保护定律还针对拉格朗日和欧拉坐标的气体动力学变量重新计算。此外，还提供了不变和保守的差异方案。
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically symmetric flows. The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. Lie group classification of this PDE is performed. Its variational structure allows to construct conservation laws with the help of Noether's theorem. These conservation laws are also recalculated for the gas dynamics variables in the Lagrangian and Eulerian coordinates. Additionally, invariant and conservative difference schemes are provided.
