We present a high-order entropy stable discontinuous Galerkin (ESDG) 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.

翻译：我们为多维领域和从一维领域建造的网络的非线性养护法提出了一个高分序稳定不连续的Galerkin(ESDG)方法,这些方法利用多维界面和网络连接的处理方法,这些处理方法在将酶稳定离散结合时保持了酶稳定性。 数字实验核查了拟议计划的稳定性,与完全实施2D的比较显示了每种连接处理的准确性。