Close Search Advanced
Journals
Resources
About Us
Open Access

A Stability Analysis of Hybrid Schemes to Cure Shock Instability

A Stability Analysis of Hybrid Schemes to Cure Shock Instability
Preview
Add to basket

Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 5 : pp. 1320–1342

Abstract

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes. By combining the Roe with HLL flux in different directions and different flux components, we give an interesting explanation to the linear numerical instability. Based on such analysis, some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.210513.091013a

Communications in Computational Physics, Vol. 15 (2014), Iss. 5 : pp. 1320–1342

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:   

  1. A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control

    Simon, Sangeeth | Mandal, J.C.

    Computers & Fluids, Vol. 174 (2018), Iss. P.144

    https://doi.org/10.1016/j.compfluid.2018.07.001 [Citations: 46]

  2. Overcoming shock instability of the HLLE-type Riemann solvers

    Liu, Liqi | Li, Xiao | Shen, Zhijun

    Journal of Computational Physics, Vol. 418 (2020), Iss. P.109628

    https://doi.org/10.1016/j.jcp.2020.109628 [Citations: 9]

  3. Modified Path-conservative HLLEM Scheme for Magnetohydrodynamic Solar Wind Simulations

    Li, Caixia | Feng, Xueshang | Li, Huichao | Wei, Fengsi

    The Astrophysical Journal Supplement Series, Vol. 253 (2021), Iss. 1 P.24

    https://doi.org/10.3847/1538-4365/abd5ab [Citations: 5]

  4. A robust low‐dissipation AUSM‐family scheme for numerical shock stability on unstructured grids

    Zhang, Fan | Liu, Jun | Chen, Biaosong | Zhong, Wanxie

    International Journal for Numerical Methods in Fluids, Vol. 84 (2017), Iss. 3 P.135

    https://doi.org/10.1002/fld.4341 [Citations: 28]

  5. A Robust Rotated-Hybrid Riemann Scheme for Multidimensional Inviscid Compressible Flows

    Tiam Kapen, Pascalin | Ghislain, Tchuen

    International Journal of Applied and Computational Mathematics, Vol. 5 (2019), Iss. 1

    https://doi.org/10.1007/s40819-019-0609-z [Citations: 2]
  6. Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere

    Cell-Centered Finite Volume Methods

    Feng, Xueshang

    2020

    https://doi.org/10.1007/978-981-13-9081-4_2 [Citations: 1]

  7. Development of a carbuncle-free and low-dissipation Roe-type scheme: Applications to multidimensional Euler flows

    Hu, Lijun | Feng, Zhaosheng

    Communications in Nonlinear Science and Numerical Simulation, Vol. 116 (2023), Iss. P.106798

    https://doi.org/10.1016/j.cnsns.2022.106798 [Citations: 5]

  8. A New Robust Carbuncle-Free Roe Scheme for Strong Shock

    Chen, Shu-sheng | Yan, Chao | Lin, Bo-xi | Li, Yan-su

    Journal of Scientific Computing, Vol. 77 (2018), Iss. 2 P.1250

    https://doi.org/10.1007/s10915-018-0747-1 [Citations: 13]

  9. Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump

    Ketcheson, David I. | Quezada de Luna, Manuel

    International Journal for Numerical Methods in Fluids, Vol. 94 (2022), Iss. 6 P.655

    https://doi.org/10.1002/fld.5070 [Citations: 2]

  10. Development of a Shock-Stable and Contact-Preserving Scheme for Multidimensional Euler Equations

    Tan, Shide | Hu, Lijun | Yuan, Haizhuan

    AIAA Journal, Vol. 60 (2022), Iss. 9 P.5232

    https://doi.org/10.2514/1.J061614 [Citations: 6]

  11. A rotated lattice Boltzmann flux solver with improved stability for the simulation of compressible flows with intense shock waves at high Mach number

    Chen, Jiabao | Yang, Dangguo | Chen, Qing | Sun, Jianhong | Wang, Yan

    Computers & Mathematics with Applications, Vol. 132 (2023), Iss. P.18

    https://doi.org/10.1016/j.camwa.2022.12.003 [Citations: 13]

  12. A modified HLLEM scheme and shock stability analysis

    Hu, Li-Jun | Yuan, Hai-Zhuan | Du, Yu-Long

    Acta Physica Sinica, Vol. 69 (2020), Iss. 13 P.134701

    https://doi.org/10.7498/aps.69.20191851 [Citations: 2]

  13. Strategies to cure numerical shock instability in the HLLEM Riemann solver

    Simon, Sangeeth | Mandal, J.C.

    International Journal for Numerical Methods in Fluids, Vol. 89 (2019), Iss. 12 P.533

    https://doi.org/10.1002/fld.4710 [Citations: 17]

  14. Numerical stability analysis of shock-capturing methods for strong shocks II: High-order finite-volume schemes

    Ren, Weijie | Xie, Wenjia | Zhang, Ye | Yu, Hang | Tian, Zhengyu

    Journal of Computational Physics, Vol. 523 (2025), Iss. P.113649

    https://doi.org/10.1016/j.jcp.2024.113649 [Citations: 0]
  15. The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018)

    Towards an Accurate and Robust Rotated Riemann Solver for Hypersonic Flow Computations

    Zhang, Ye | Li, Hua | Xie, W. J. | Zhang, Ran

    2019

    https://doi.org/10.1007/978-981-13-3305-7_53 [Citations: 0]

  16. A stable hybrid Roe scheme on triangular grids

    Phongthanapanich, Sutthisak

    International Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 4 P.978

    https://doi.org/10.1002/fld.4916 [Citations: 7]

  17. An Accurate and Robust Line-Hybrid Method for Hypersonic Heating Predictions

    Zhang, Ye | Xie, Wenjia | Ren, Weijie | Tian, Zhengyu

    International Journal of Computational Fluid Dynamics, Vol. 37 (2023), Iss. 5 P.395

    https://doi.org/10.1080/10618562.2023.2296536 [Citations: 1]

  18. An accurate and robust HLLC‐type Riemann solver for the compressible Euler system at various Mach numbers

    Xie, Wenjia | Zhang, Ran | Lai, Jianqi | Li, Hua

    International Journal for Numerical Methods in Fluids, Vol. 89 (2019), Iss. 10 P.430

    https://doi.org/10.1002/fld.4704 [Citations: 29]

  19. Evaluation of rotated upwind schemes for contact discontinuity and strong shock

    Zhang, Fan | Liu, Jun | Chen, Biaosong | Zhong, Wanxie

    Computers & Fluids, Vol. 134-135 (2016), Iss. P.11

    https://doi.org/10.1016/j.compfluid.2016.05.010 [Citations: 21]

  20. A robust HLLC-type Riemann solver for strong shock

    Shen, Zhijun | Yan, Wei | Yuan, Guangwei

    Journal of Computational Physics, Vol. 309 (2016), Iss. P.185

    https://doi.org/10.1016/j.jcp.2016.01.001 [Citations: 60]

  21. A unified construction of all-speed HLL-type schemes for hypersonic heating computations

    Xie, Wenjia | Tian, Zhengyu | Zhang, Ye | Yu, Hang | Ren, Weijie

    Computers & Fluids, Vol. 233 (2022), Iss. P.105215

    https://doi.org/10.1016/j.compfluid.2021.105215 [Citations: 4]

  22. A robust and contact preserving flux splitting scheme for compressible flows

    Hu, Lijun | Feng, Sebert

    Communications in Nonlinear Science and Numerical Simulation, Vol. 93 (2021), Iss. P.105502

    https://doi.org/10.1016/j.cnsns.2020.105502 [Citations: 6]

  23. MSAT: Matrix stability analysis tool for shock-capturing schemes

    Ren, Weijie | Xie, Wenjia | Zhang, Ye | Yu, Hang | Tian, Zhengyu

    SoftwareX, Vol. 24 (2023), Iss. P.101566

    https://doi.org/10.1016/j.softx.2023.101566 [Citations: 2]

  24. A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

    Vevek, U. S. | Zang, B. | New, T. H.

    Applied Mathematics and Mechanics, Vol. 42 (2021), Iss. 9 P.1259

    https://doi.org/10.1007/s10483-021-2762-6 [Citations: 5]

  25. A simple cure for numerical shock instability in the HLLC Riemann solver

    Simon, Sangeeth | Mandal, J.C.

    Journal of Computational Physics, Vol. 378 (2019), Iss. P.477

    https://doi.org/10.1016/j.jcp.2018.11.022 [Citations: 41]

  26. Numerical stability analysis of Godunov-type schemes for high Mach number flow simulations

    Ren, Weijie | Xie, Wenjia | Zhang, Ye | Yu, Hang | Tian, Zhengyu | Zhu, Jiajun

    Physics of Fluids, Vol. 36 (2024), Iss. 6

    https://doi.org/10.1063/5.0210632 [Citations: 0]

  27. On numerical instabilities of Godunov-type schemes for strong shocks

    Xie, Wenjia | Li, Wei | Li, Hua | Tian, Zhengyu | Pan, Sha

    Journal of Computational Physics, Vol. 350 (2017), Iss. P.607

    https://doi.org/10.1016/j.jcp.2017.08.063 [Citations: 47]

  28. Further studies on numerical instabilities of Godunov-type schemes for strong shocks

    Xie, Wenjia | Tian, Zhengyu | Zhang, Ye | Yu, Hang | Ren, Weijie

    Computers & Mathematics with Applications, Vol. 102 (2021), Iss. P.65

    https://doi.org/10.1016/j.camwa.2021.10.008 [Citations: 8]

  29. On the carbuncle instability of the HLLE-type solvers

    Shen, Zhijun | Ren, Jian | Cui, Xia

    Journal of Physics: Conference Series, Vol. 1290 (2019), Iss. 1 P.012026

    https://doi.org/10.1088/1742-6596/1290/1/012026 [Citations: 1]

  30. A shock-stable numerical scheme accurate for contact discontinuities: Applications to 3D compressible flows

    Hu, Lijun | Wang, Xiaohui

    Communications in Nonlinear Science and Numerical Simulation, Vol. 128 (2024), Iss. P.107602

    https://doi.org/10.1016/j.cnsns.2023.107602 [Citations: 0]