Three dimensional HLL Riemann solver for conservation laws on structured meshes; Application to Euler and magnetohydrodynamic flows
Three dimensional HLL Riemann solver for conservation laws on structured meshes; Application to Euler and magnetohydrodynamic flows
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DOI：
10.1016/j.jcp.2015.03.056
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发表时间：
2015-08-15
影响因子：
4.1
通讯作者：
Balsara, Dinshaw S.
中科院分区：
文献类型：
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作者：
Balsara, Dinshaw S.
在本文中，我们建立在我们以前的多维黎曼解算器的工作，详细介绍了三维HLL黎曼解算器的建设。与二维黎曼解算器一样，这是通过在所考虑的状态之间引入一个常数解析状态来实现的，这为守恒律系统引入了足够的耗散。解析通量的封闭形式的表达式，以方便数值实现。这是通过引入一个新的推导多维黎曼解算器。新奇包括集成拉格朗日通量移动表面。这使得问题更容易在三维空间中可视化。（多维Riemann解算器的视频介绍可在http://www.nd.edu/similar上访问dbalsara/Numerical-PDE-Course。）本文提出了一种求解三维欧拉和磁流体流动的二阶精度数值格式。该计划是建立在当前的三维黎曼求解器，并已实施在作者的RIEMANN代码。我们证明，该计划的基础上的三维黎曼求解器允许多维的不连续性传播更各向同性的分辨率饥饿网格。每秒更新的区域的数量由这个计划在现代处理器上被证明是具有成本竞争力的计划，是基于一维黎曼解算器。然而，本计划允许更大的时间步长在三维，因为它包括真正的三维流动的影响。对于MHD问题，在计算边缘中心电场时，没有必要将耗散加倍。对三维欧拉问题和磁流体问题的精度分析表明，该格式满足设计精度。还提出了几个严格的测试问题，涉及欧拉和MHD流和该计划的执行鲁棒性对所有这些。第一次，我们提出了三维黎曼问题的制定和解决方案。(C)2015 Elsevier Inc. All rights reserved.
In this paper we build on our prior work on multidimensional Riemann solvers by detailing the construction of a three-dimensional HLL Riemann solver. As with the two-dimensional Riemann solver, this is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are provided to facilitate numerical implementation. This is accomplished by introducing a novel derivation of the multidimensional Riemann solver. The novelty consists of integrating Lagrangian fluxes across moving surfaces. This makes the problem easier to visualize in three dimensions. (A video introduction to multidimensional Riemann solvers is available on http://www.nd.edu/similar to dbalsara/Numerical-PDE-Course.)A robust and efficient second order accurate numerical scheme for three dimensional Euler and MHD flows is presented. The scheme is built on the current three-dimensional Riemann solver and has been implemented in the author's RIEMANN code. We demonstrate that schemes that are based on the three-dimensional Riemann solver permit multidimensional discontinuities to propagate more isotropically on resolution-starved meshes. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps in three dimensions because of its inclusion of genuinely three-dimensional effects in the flow. For MHD problems it is not necessary to double the dissipation when evaluating the edge-centered electric fields. Accuracy analysis for three-dimensional Euler and MHD problems shows that the scheme meets its design accuracy. Several stringent test problems involving Euler and MHD flows are also presented and the scheme is shown to perform robustly on all of them. For the very first time, we present the formulation and solution of three-dimensional Riemann problems. (C) 2015 Elsevier Inc. All rights reserved.