On discretely entropy conservative and entropy stable discontinuous Galerkin methods
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
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DOI：
10.1016/j.jcp.2018.02.033
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发表时间：
2018-06-01
影响因子：
4.1
通讯作者：
Chan, Jesse
中科院分区：
文献类型：
--
作者：
Chan, Jesse
基于部分算子对角范数求和的高阶方法可以证明满足非线性双曲型偏微分方程组的离散熵守恒或耗散[1，2]。这些方法也可以解释为具有对角质量矩阵的节点间断Galerkin方法[3-6]。在这项工作中，我们描述了如何使用通量差分，基于正交的投影，和类似SBP的运营商构建离散熵守恒方案DG方法下更任意选择的体积和表面求积规则。所得到的方法是半离散熵保守或熵稳定的体积求积规则。数值实验验证了本文方法的稳定性和高精度。(C)2018爱思唯尔公司All rights reserved.
High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs [1,2]. These methods can also be interpreted as nodal discontinuous Galerkin methods with diagonal mass matrices [3-6]. In this work, we describe how use flux differencing, quadrature-based projections, and SBP-like operators to construct discretely entropy conservative schemes for DG methods under more arbitrary choices of volume and surface quadrature rules. The resulting methods are semi-discretely entropy conservative or entropy stable with respect to the volume quadrature rule used. Numerical experiments confirm the stability and high order accuracy of the proposed methods for the compressible Euler equations in one and two dimensions. (C) 2018 Elsevier Inc. All rights reserved.