We present a high-order entropy stable discontinuous Galerkin method for nonlinear conservation laws on both multi-dimensional domains and on networks constructed from one-dimensional domains. These methods utilize treatments of multi-dimensional interfaces and network junctions which retain entropy stability when coupling together entropy stable discretizations. Numerical experiments verify the stability of the proposed schemes, and comparisons with fully 2D implementations demonstrate the accuracy of each type of junction treatment.

中文翻译：

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网络和多维域上非线性守恒律的熵稳定不连续Galerkin方法

我们针对多维域和从一维域构造的网络上的非线性守恒定律提出了一种高阶熵稳定不连续Galerkin方法。这些方法利用多维接口和网络结的处理，当将熵稳定的离散化耦合在一起时，这些接口保留了熵的稳定性。数值实验验证了所提出方案的稳定性，并且与完全2D实现方案的比较证明了每种类型的结处理的准确性。