非结构高阶CPR方法的子单元限制中的问题单元侦测  

Troubled cell detection in subcell limiting for high-order CPR method on unstructured meshes

作　　者：石国权 燕振国 朱华君 马燕凯 贾斐然 SHI Guoquan;YAN Zhenguo;ZHU Huajun;MA Yankai;JIA Feiran(State Key Laboratory of Aerodynamics,Mianyang 621000,China;School of Power and Energy,Northwestern Polytechnical University,Xi’an 710000,China)

机构地区：[1]空气动力学国家重点实验室,绵阳621000 [2]西北工业大学动力与能源学院,西安710000

出　　处：《空气动力学学报》2023年第2期38-52,I0001,共16页Acta Aerodynamica Sinica

基　　金：国家数值风洞工程(NNW);国家自然科学基金(12172375,11902344);空气动力学国家重点实验室基金(SKLA2019010101)。

摘　　要：重构修正(correction procedure via reconstruction, CPR)是一种计算高效、模板紧致、适用于非结构网格的高阶方法,但是无法处理流场含有较强间断的问题。针对这个问题,前期基于二阶非等距非线性加权插值的激波捕捉格式以及非结构四边形网格,发展了高阶CPR方法的一种子单元限制技术。该技术首先通过侦测因子确定出问题单元,然后将问题单元基于CPR求解点划分成非等距子单元,并在子单元中采用二阶激波捕捉格式进行计算。这种子单元限制技术保证了主单元和子单元的求解点重合,可以十分方便地处理主单元和子单元之间的数据交换。问题单元的侦测是该子单元限制技术的关键步骤,侦测出的问题单元的数量以及分布情况都将会影响数值结果。基于此,本文同时考虑了单元侦测和分维侦测两种问题单元侦测方式。通过激波管问题、Shu-Osher问题、双马赫反射问题、激波-旋涡干扰等典型算例对比分析了TVB、MDHE和JST侦测因子对数值格式分辨率的影响。研究结果表明:分维侦测能够减少问题单元的区域,进而提高分辨率。The correction procedure via reconstruction(CPR) method is an efficient and compact method,suitable for unstructured meshes, but it cannot solve the problem with strong discontinuities in flow fields. Based on the shock-capturing scheme with second-order non-uniform nonlinear weighted interpolation, we previously developed a subcell limiting technique for the high-order CPR method on two-dimensional unstructured quadrilateral meshes. Within this technique, the troubled cells are first divided into non-uniform subcells, then a second-order shock-capturing scheme is adopted for the calculation. As the solution points are overlaid between the main cells and the subcells, it is very convenient to handle the data exchange in the two layers. The detection of troubled cells is a crucial step in the subcell limiting technique, and the number and distribution of troubled cells can both affect the numerical results. Based on this, the present study considers two methods of troubled cell detecting, i.e. detecting by cell and detecting by dimension. This paper compares and analyzes the influence of different indicators, i.e. TVB, MDH, and JST, on the resolution of numerical schemes through typical benchmark cases such as the shock tube problem, the Shu-Osher problem, the double Mach reflection problem, and the shock-vortex interaction. The results show that detecting by dimension can reduce the number of troubled cells,thereby improving the resolution, which has a certain scientific value.

关 键 词：高阶CPR方法 子单元限制 问题单元侦测 分维侦测 激波捕捉格式 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]