High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
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DOI：
10.1016/j.jcp.2003.08.023
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发表时间：
2004-01-20
影响因子：
4.1
通讯作者：
Tenaud, C
中科院分区：
文献类型：
--
作者：
Daru, V;Tenaud, C
本文致力于开发一种用于非定常可压缩流数值模拟的精确一步法。继续我们在达鲁和特诺的工作 [V. Darn, C. Tenaud，计算机。 Fluids 30 (2001) 89]在考虑三阶格式的情况下，我们遵循Lax-Wendroff方法通过修正连续的修正方程来开发高阶TVD组合时空格式。在标量情况下，获得了时间和空间上精确到七阶 (OSTVD7) 的 TVD 方案（在平滑区域并远离极值）。为了避免极值附近 TVD 方案常见的削波和精度损失，我们开发了从 Suresh 和 Huynh [A.苏雷什，HT。 Huynh，J. 计算机。物理。 136 (1997) 83] 局部放松对这一族一步式方案的 TVD 限制。标量情况下长时间积分的数值结果表明，与包括 WENO 方案在内的几种多级方案相比，MP 一步法给出了最佳结果。对系统和多维情况的扩展是以简化的方式完成的，这种方式不保留精度的标量顺序。然而，我们表明所得到的方案的错误率非常低。为了验证，本算法已经在几个经典的一维和多维测试用例上进行了检查，包括粘性和无粘流：与正弦波相互作用的移动冲击波、Lax激波管问题、二维无粘性双马赫反射和二维粘性冲击波涡旋相互作用。通过计算这些不同的测试用例，我们证明使用一步 MP 方法可以获得非常准确的结果，与多级高阶方案相比，该方法非常有竞争力。 (C) 2003 Elsevier B.V. 保留所有权利。
This paper deals with the development of accurate one-step schemes for the numerical simulation of unsteady compressible flows. Pursuing our work in Daru and Tenaud [V. Darn, C. Tenaud, Comput. Fluids 30 (2001) 89] where third-order schemes were considered, we follow the Lax-Wendroff approach to develop high order TVD combined time-space schemes by correcting the successive modified equations. In the scalar case, TVD schemes accurate up to seventh order (OSTVD7) in time and space are obtained (in smooth regions and away from extrema). To avoid the clipping and the loss of accuracy that is common to the TVD schemes near extrema, we develop monotonicity-preserving (MP) conditions derived from Suresh and Huynh [A. Suresh, HT. Huynh, J. Comput. Phys. 136 (1997) 83] to locally relax the TVD limitation for this family of one-step schemes. Numerical results for long time integration in the scalar case show that the MP one-step approach gives the best results compared to several multistage schemes, including WENO schemes. The extension to systems and to the multidimensional case is done in a simplified way which does not preserve the scalar order of accuracy. However we show that the resulting schemes have a very low level of error. For validation, the present algorithm has been checked on several classical one-dimensional and multidimensional test cases, including both viscous and inviscid flows: a moving shock wave interacting with a sine wave, the Lax shock tube problem, the 2D inviscid double Mach reflection and the 2D viscous shock wave vortex interaction. By computing these various test cases, we demonstrate that very accurate results can be obtained by using the one-step MP approach which is very competitive compared to multistage high order schemes. (C) 2003 Elsevier B.V. All rights reserved.