Abstract

The variational approach to obtaining equations of the entropy stable discontinuous Galerkin method is generalized. It is shown how the monotonicity property can be incorporated into this approach. As applied to Euler equations, the entropic slope limiter, a new effective approximate method for the studied approach, is designed. It guarantees the monotonicity of the numerical solution, as well as the nonnegativity of the pressure and entropy production for each finite element. This method is successfully tested on some well-known gas dynamics model problems.

中文翻译：

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Euler方程的带有熵斜率限制器的间断Galerkin方法

摘要

归纳了变分求解熵稳定不连续Galerkin方法方程的方法。它显示了如何将单调性合并到此方法中。将熵斜率限制器应用于欧拉方程，设计了一种新的有效近似方法。它保证了数值解的单调性，以及每个有限元的压力和熵产生的非负性。该方法已在一些著名的气体动力学模型问题上成功测试。