Abstract

A conservative version of the entropy stable discontinuous Galerkin method is proposed for the Euler equations in variables: density, momentum density, and pressure. For the equation describing the dynamics of the mean pressure in an FE, a special difference approximation in time and conservative in total energy is constructed. The entropy inequality and the requirements for the monotonicity of the numerical solution are satisfied by a special slope limiter. The developed method is successfully tested on a number of model gas-dynamic problems. In particular, in the numerical solution of the Einfeldt problem, the quality of the calculation of the specific internal energy is significantly improved.

中文翻译：

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使用非保守变量的 Euler 方程的熵稳定不连续 Galerkin 方法

摘要

熵稳定不连续伽辽金方法的保守版本被提议用于变量中的欧拉方程：密度、动量密度和压力。对于描述有限元中平均压力动力学的方程，构建了一个特殊的时间差异近似值和总能量保守值。熵不等式和数值解的单调性要求由一个特殊的斜率限制器来满足。开发的方法在许多模型气体动力学问题上得到了成功的测试。特别是在Einfeldt问题的数值解中，比内能的计算质量得到了显着提高。