非结构高阶CPR方法的子单元限制中的问题单元侦测

石国权; 燕振国; 朱华君; 马燕凯; 贾斐然

doi:10.7638/kqdlxxb-2021.0406

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

非结构高阶CPR方法的子单元限制中的问题单元侦测

研究论文 | 更新时间：2026-05-28

- 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
- 空气动力学学报 2023年41卷第2期页码：38-52
- 作者机构：
  
  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
- 作者简介：
  
  石国权（1997-），男，河南人，硕士，研究方向：计算流体力学中的高精度算法及应用. E-mail：sgquan@buaa.edu.cn
  朱华君*（1982-），女，浙江人，博士，副研究员，研究方向：计算流体力学中的高精度算法及应用. E-mail：zhuhjgirl@163.com
- 基金信息：
  
  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）
- DOI：10.7638/kqdlxxb-2021.0406
  中图分类号： V211.3
- 纸质出版：2023
- 稿件说明：
移动端阅览
石国权, 燕振国, 朱华君, 等. 非结构高阶CPR方法的子单元限制中的问题单元侦测[J]. 空气动力学学报, 2023, 41(2): 38−52.

SHI Guoquan, YAN Zhenguo, ZHU Huajun, et al. Troubled cell detection in subcell limiting for high-order CPR method on unstructured meshes[J]. 2023, 41(2): 38-52.
石国权, 燕振国, 朱华君, 等. 非结构高阶CPR方法的子单元限制中的问题单元侦测[J]. 空气动力学学报, 2023, 41(2): 38−52. DOI： 10.7638/kqdlxxb-2021.0406

SHI Guoquan, YAN Zhenguo, ZHU Huajun, et al. Troubled cell detection in subcell limiting for high-order CPR method on unstructured meshes[J]. 2023, 41(2): 38-52. DOI： 10.7638/kqdlxxb-2021.0406.

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。

Abstract

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

Keywords

references

WANG Z J. High-order methods for the Euler and navier-stokes equations on unstructured grids[J]. Progress in Aerospace Sciences, 2007, 43(1-3): 1-41. DOI:10.1016/j.paerosci.2007.05.001

ZHANG L P, HE L X, LIU W, et al. Reviews of high-order methods on unstructured and hybrid grid[J]. Advances in Mechanics, 2013, 43(2): 202-236. (in Chinese)

HUYNH H T. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods[C]//Proc of the 18th AIAA Computational Fluid Dynamics Conference, Miami, Florida. Reston, Virigina: AIAA, 2007: 1-42. doi: 10.2514/6.2007-4079

WANG Z J, GAO H Y. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids[J]. Journal of Computational Physics, 2009, 228(21): 8161-8186. DOI:10.1016/j.jcp.2009.07.036

WANG Z J, GAO H Y, HAGA T. A unifying discontinuous CPR formulation for the Navier–Stokes equations on mixed grids[C]//Computational Fluid Dynamics 2010, 2011: 59-65. doi: 10.1007/978-3-642-17884-9_5

VONNEUMANN J, RICHTMYER R D. A method for the numerical calculation of hydrodynamic shocks[J]. Journal of Applied Physics, 1950, 21(3): 232-237. DOI:10.1063/1.1699639

PERSSON P O, PERAIRE J. Sub-cell shock capturing for discontinuous Galerkin methods[C]// 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. Reston, Virigina: AIAA, 2006: 1-13. doi:10.2514/6.2006-112

YU J, YAN C. Discontinuous Galerkin method based on artificial viscosity[J]. Acta Aerodynamica Sinica, 2013, 31(3): 371-375. (in Chinese)

ZHU J, ZHONG X H, SHU C W, et al. Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes[J]. Journal of Computational Physics, 2013, 248: 200-220. DOI:10.1016/j.jcp.2013.04.012

KIM K H, KIM C. Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows: part I: spatial discretization[J]. Journal of Computational Physics, 2005, 208(2): 527-569. DOI:10.1016/j.jcp.2005.02.021

MICHALAK C, OLLIVIER-GOOCH C. Accuracy preserving limiter for the high-order accurate solution of the Euler equations[J]. Journal of Computational Physics, 2009, 228(23): 8693-8711. DOI:10.1016/j.jcp.2009.08.021

QIU J X, SHU C W. A comparison of troubled-cell indicators for runge: kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters[J]. SIAM Journal on Scientific Computing, 2005, 27(3): 995-1013. DOI:10.1137/04061372x

ZHANG F, ZHANG L D, LIU J, et al. Hybrid TV-van leer upwind scheme on unstructured grids[J]. Acta Aerodynamica Sinica, 2019, 37(5): 855-863. (in Chinese)

PARK J S, KIM C. Hierarchical multi-dimensional limiting strategy for correction procedure via reconstruction[J]. Journal of Computational Physics, 2016, 308: 57-80. DOI:10.1016/j.jcp.2015.12.020

N. Discacciati, J. S. Hesthaven, D. Ray. Cotrolling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neuralnet works[J]. Journal of Computational Physics, 2020, 409: 109304. DOI:10.1016/j.jcp.2020.109304

LI Y N, WANG Z J. A convergent and accuracy preserving limiter for the FR/CPR method[C]//Proc of the 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas. Reston, Virginia: AIAA, 2017: 1-16. doi: 10.2514/6.2017-0756

DU J, SHU C W, ZHANG M P. A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework[J]. Applied Numerical Mathematics, 2015, 95: 173-198. DOI:10.1016/j.apnum.2014.01.006

HUERTA A, CASONI E, PERAIRE J. A simple shock-capturing technique for high-order discontinuous Galerkin methods[J]. International Journal for Numerical Methods in Fluids, 2012, 69(10): 1614-1632. DOI:10.1002/fld.2654

DUMBSER M, ZANOTTI O, LOUBÈRE R, et al. A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws[J]. Journal of Computational Physics, 2014, 278: 47-75. DOI:10.1016/j.jcp.2014.08.009

DUMBSER M, LOUBÈRE R. A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes[J]. Journal of Computational Physics, 2016, 319: 163-199. DOI:10.1016/j.jcp.2016.05.002

KOCHI S R S P, RAMAKRISHNA M. A compact subcell WENO limiting strategy using immediate neighbors for runge-kutta discontinuous Galerkin methods for unstructured meshes[J]. Journal of Scientific Computing, 2021, 90(1): 1-24. DOI:10.1007/s10915-021-01725-3

GUO J, ZHU H J, YAN Z G, et al. High-order hybrid WCNS-CPR scheme for shock capturing of conservation laws[J]. International Journal of Aerospace Engineering, 2020, 2020: 1-13. DOI:10.1155/2020/8825445

HENNEMANN S, RUEDA-RAMÍREZ A M, HINDENLANG F J, et al. A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations[J]. Journal of Computational Physics, 2021, 426: 109935. DOI:10.1016/j.jcp.2020.109935

SONNTAG M, MUNZ C D. Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells[J]. Journal of Scientific Computing, 2017, 70(3): 1262-1289. DOI:10.1007/s10915-016-0287-5

ZHU H J, LIU H Y, YAN Z G, et al. Shock capturing schemes based on nonuniform nonlinear weighted interpolation for conservation laws and their application as subcell limiters for FR/CPR[J]. 2021: arXiv: 2107.06471 [math. NA].

COCKBURN B, SHU C W. TVB runge-kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework[J]. Mathematics of Computation, 1989, 52(186): 411-435.

KLÖCKNER A, WARBURTON T, HESTHAVEN J S. Viscous shock capturing in a time-explicit discontinuous Galerkin method[J]. Mathematical Modelling of Natural Phenomena, 2011, 6(3): 57-83. DOI:10.1051/mmnp/20116303

FU D X, MA Y W. Computational Fluid Dynamics[M]. Beijing: Higher Education Press, 2002(in Chinese).

LI W, WANG Q, REN Y X. A p-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids[J]. Journal of Computational Physics, 2020, 407: 109246

WANG C S. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws[R]. 1997. doi: 10.1023/A: 1025316311633

RAULT A, CHIAVASSA G, DONAT R. Shock-vortex interactions at high Mach numbers[J]. Journal of Scientific Computing, 2003, 19(1-3): 347-371

LU Q L, LIU G M, MING P J, et al. A parameter-free gradient-based limiter for the FR/CPR method on mixed unstructured meshes[C]//Proc of the AIAA Aviation 2019 Forum, Dallas, Texas. Reston, Virginia: AIAA, 2019. doi: 10.2514/6.2019-3210

LUO X, WU S P. An improved fifth-order weno-z+ scheme[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1927-1939. (in Chinese)

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

个体间距对多扑翼气动噪声的影响特性

某型电动跑车尾翼气动设计的仿真与试验研究

水滴撞击运动超疏水表面特性及其调控

热防护材料动态烧蚀形貌结构光视觉测量技术

安装效应对螺旋桨纯音噪声的影响