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首页> 外文期刊>Journal of Computational Physics >Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations
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Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

机译：双曲型非守恒偏微分方程的间断Galerkin有限元方法。

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摘要

We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium. we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products. (C) 2007 Elsevier Inc. All rights reserved.
机译：我们提出时空不连续的Galerkin有限元（DGFEM）公式，用于包含非保守乘积的系统，例如出现在分散多相流方程中的系统。主要标准。我们对弱公式提出的假设是，如果非保守偏微分方程组可以转化为保守形式，则该公式必须简化为保守系统的形式。标准DGFEM公式不能应用于偏微分方程的非保守系统。因此，我们将非保守产品的弱解理论引入DGFEM公式，从而提出了一个新问题，即如何定义在不连续处连接左右状态的路径。研究了不同路径对数值解的影响，发现该影响很小。我们还介绍了一种能够处理非保守产品的新数值通量。我们的方案适用于两个不同的偏微分方程系统。首先，我们考虑浅水方程，其中地形导致非保守积，其中已知的（可能是不连续的）地形被正式视为系统中的未知数。其次，我们考虑简化包含多个固有非保守乘积的深度平均两相流模型。 （C）2007 Elsevier Inc.保留所有权利。

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