Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
复制标题
高效实施守恒定律的高阶逆 Lax-Wendroff 边界处理
DOI：
10.1016/j.jcp.2011.11.037
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发表时间：
2012-03-20
影响因子：
4.1
通讯作者：
Ning, Jianguo
中科院分区：
文献类型：
--
作者：
Tan, Sirui;Wang, Cheng;Ning, Jianguo
在文献[20]中，两位作者发展了一种求解双曲型守恒律方程的高精度数值边界条件方法，该方法允许在笛卡尔网格上使用高阶有限差分格式求解边界与网格线不重合的任意物理区域中的问题。该程序是基于所谓的逆Lax-Wendroff（ILW）程序的流入边界条件和高阶外推的流出边界条件。然而，ILW过程的代数对于二维（2D）双曲系统是相当繁重的，这使得难以实现精度高于三阶的过程。在本文中，我们首先讨论了一个简化和改进的实现这一过程，它使用相对复杂的ILW程序只计算一阶法向导数。五阶韦诺型外推用于所有其他导数，而不管局部特征的方向和解的光滑度。这使得五阶边界处理的实现对于具有源项的2D系统是实用的。对于可压缩无粘流动的无穿透边界条件，本文讨论了一种进一步的简化方法，避免了ILW方法中涉及的切向导数的计算。我们测试我们的简化和改进的边界处理的欧拉方程，或没有源项表示在爆炸中的化学反应。结果表明，所设计的五阶精度，稳定性和良好的性能，涉及爆轰/冲击波和固体边界之间的复杂相互作用的问题。(C)2011 Elsevier Inc. All rights reserved.
In [20], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax-Wendroff (ILW) procedure for inflow boundary conditions and high order extrapolation for outflow boundary conditions. However, the algebra of the ILW procedure is quite heavy for two dimensional (2D) hyperbolic systems, which makes it difficult to implement the procedure for order of accuracy higher than three. In this paper, we first discuss a simplified and improved implementation for this procedure, which uses the relatively complicated ILW procedure only for the evaluation of the first order normal derivatives. Fifth order WENO type extrapolation is used for all other derivatives, regardless of the direction of the local characteristics and the smoothness of the solution. This makes the implementation of a fifth order boundary treatment practical for 2D systems with source terms. For no-penetration boundary condition of compressible inviscid flows, a further simplification is discussed, in which the evaluation of the tangential derivatives involved in the ILW procedure is avoided. We test our simplified and improved boundary treatment for Euler equations with or without source terms representing chemical reactions in detonations. The results demonstrate the designed fifth order accuracy, stability, and good performance for problems involving complicated interactions between detonation/shock waves and solid boundaries. (C) 2011 Elsevier Inc. All rights reserved.