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首页> 外文期刊>Journal of Computational Physics >Combined Hybridizable Discontinuous Galerkin (HDG) and Runge-Kutta Discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes
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Combined Hybridizable Discontinuous Galerkin (HDG) and Runge-Kutta Discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes

机译：合并杂交的不连续的Galerkin（HDG）和Runge-Kutta不连续的Galerkin（RK-DG）在非结构化网眼上的绿色Naghdi方程式配方

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In this paper, we introduce some new high-order discrete formulations on general unstructured meshes, especially designed for the study of irrotational free surface flows based on partial differential equations belonging to the family of fully nonlinear and weakly dispersive shallow water equations. Working with a recent family of optimized asymptotically equivalent equations, we benefit from the simplified analytical structure of the linear dispersive operators to conveniently reformulate the models as the classical nonlinear shallow water equations supplemented with several algebraic source terms, which globally account for the non-hydrostatic effects through the introduction of auxiliary coupling variables. High-order discrete approximations of the main flow variables are obtained with a RK-DG method, while the trace of the auxiliary variables are approximated on the mesh skeleton through the resolution of second-order linear elliptic sub-problems with high-order HDG formulations. The combined use of hybrid unknowns and local post-processing significantly helps to reduce the number of globally coupled unknowns in comparison with previous approaches. The proposed formulation is then extended to a more complex family of three parameters enhanced Green-Naghdi equations. The resulting numerical models are validated through several benchmarks involving nonlinear waves transformations and propagation over varying topographies, showing good convergence properties and very good agreements with several sets of experimental data. (C) 2020 Elsevier Inc. All rights reserved.
机译：在本文中，我们介绍了一般非结构化网眼的一些新的高阶离散制剂，特别是基于属于全非线性和弱分散浅水方程系列的部分微分方程的局部微分方程研究了对无检测自由表面流动的研究。使用最近的优化渐近等效等式的家庭，我们受益于线性分散操作者的简化分析结构，方便地重构模型作为典型的非线性浅水方程，其补充有几个代数源术语，这些源术语全球占非静液压通过引入辅助耦合变量来实现。通过RK-DG方法获得主流量变量的高阶离散近似，而通过高阶HDG配方的二阶线性椭圆亚问题的分辨率，辅助变量的迹线近似于网格骨架上。混合杂交品未知和本地后处理的结合使用显着有助于减少与先前方法相比的全球耦合未知数的数量。然后将所提出的配方扩展到更复杂的三个参数系列增强的绿色Naghdi方程。通过涉及非线性波形变换和传播在不同的地形上的若干基准验证了所得到的数值模型，显示出良好的收敛性和与几组实验数据的良好协议。 （c）2020 Elsevier Inc.保留所有权利。

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