A characteristic space-time conservation element and solution element method for conservation laws
A characteristic space-time conservation element and solution element method for conservation laws
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一种特征时空守恒元及守恒律解元法
DOI：
10.1016/j.jcp.2015.02.018
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发表时间：
2015-05
影响因子：
4.1
通讯作者：
Zhang De-Liang
中科院分区：
文献类型：
--
作者：
Shen Hua;Wen Chih-Yung;Zhang De-Liang
本文发展了一种求解守恒律的迎风时空守恒元/解元方法。该方法将网格数和空间导数作为独立的推进变量，与Chang（1995）[5]提出的CE/SE方法一致。交错时间推进策略和守恒元的定义也遵循张的命题。然而，解元（SE）的定义是从张的定义修改。通过两个不同的守恒单元的界面的数值通量不是直接由反时间方向上的泰勒展开张的建议，而是由一个迎风程序确定。这种修改并没有改变原方法的局部和全局保守性。虽然网格变量的时间推进格式与原方法相同，但在空间导数的计算中加入了迎风通量，从而得到了与Chang方法完全不同的方法。迎风格式打破了原格式的时空反演不变性，使新格式可以直接用于捕捉间断，而不会产生虚假振荡。此外，本方法在CFL数的宽范围内（从10 - 6到1）保持低耗散。进一步，我们将迎风CE/SE方法推广到求解Euler方程，采用了三种不同的近似Riemann解：Harten、Lax和货车Leer（HLL）Riemann解、接触不连续恢复HLLC Riemann解和数学上严格的Roe Riemann解。大量的数值例子进行了证明本方法的鲁棒性。数值结果表明，新的CE/SE求解器执行改进的分辨率。
In this paper, an upwind space–time conservation element and solution element (CE/SE) method is developed to solve conservation laws. In the present method, the mesh quantity and spatial derivatives are the independent marching variables, which is consistent with the original CE/SE method proposed by Chang (1995)[5]. The staggered time marching strategy and the definition of conservation element (CE) also follow Chang's propositions. Nevertheless, the definition of solution element (SE) is modified from that of Chang. The numerical flux through the interface of two different conservation elements is not directly derived by a Taylor expansion in the reversed time direction as proposed by Chang, but determined by an upwind procedure. This modification does not change the local and global conservative features of the original method. Although, the time marching scheme of mesh variables is the same with the original method, the upwind fluxes are involved in the calculation of spatial derivatives, yielding a totally different approach from that of Chang's method. The upwind procedure breaks the space–time inversion invariance of the original scheme, so that the new scheme can be directly applied to capture discontinuities without spurious oscillations. In addition, the present method maintains low dissipation in a wide range of CFL number (from 10− 6 to 1). Furthermore, we extend the upwind CE/SE method to solve the Euler equations by adopting three different approximate Riemann solvers including Harten, Lax and van Leer (HLL) Riemann solver, contact discontinuity restoring HLLC Riemann solver and mathematically rigorous Roe Riemann solver. Extensive numerical examples are carried out to demonstrate the robustness of the present method. The numerical results show that the new CE/SE solvers perform improved resolutions.
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影响因子：
6.5
作者：
G. D. V. Albada;B. Leer;W. Roberts
通讯作者：
G. D. V. Albada;B. Leer;W. Roberts
影响因子：
2.2
作者：
E. Toro;M. Spruce;W. Speares
通讯作者：
E. Toro;M. Spruce;W. Speares
DOI：
10.2514/6.2005-4355
发表时间：
2013-07
期刊：
--
影响因子：
--
作者：
Sin-Chung Chang
通讯作者：
Sin-Chung Chang
影响因子：
10.2
作者：
A. Harten;P. Lax;B. Leer
通讯作者：
A. Harten;P. Lax;B. Leer
DOI：
10.1016/j.jcp.2011.06.018
发表时间：
2011-09
期刊：
J. Comput. Phys.
影响因子：
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作者：
Wanai Li;Yu-xin Ren;Guodong Lei;H. Luo
通讯作者：
Wanai Li;Yu-xin Ren;Guodong Lei;H. Luo