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一种基于TV分裂的真正多维Riemann解法器

胡立军 袁礼

胡立军, 袁礼. 一种基于TV分裂的真正多维Riemann解法器[J]. 应用数学和力学, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207
引用本文: 胡立军, 袁礼. 一种基于TV分裂的真正多维Riemann解法器[J]. 应用数学和力学, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207
HU Li-jun, YUAN Li. A Genuinely Multidimensional Riemann Solver Based on the TV Splitting[J]. Applied Mathematics and Mechanics, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207
Citation: HU Li-jun, YUAN Li. A Genuinely Multidimensional Riemann Solver Based on the TV Splitting[J]. Applied Mathematics and Mechanics, 2017, 38(3): 243-264. doi: 10.21656/1000-0887.370207

一种基于TV分裂的真正多维Riemann解法器

doi: 10.21656/1000-0887.370207
基金项目: 国家重点基础研究发展计划(973计划)(2010CB731505); 国家自然科学基金(11321061);国家自然科学基金国际(地区)合作交流项目(NSFC-RGC11261160486)
详细信息
    作者简介:

    胡立军(1985—),男,博士生(通讯作者. E-mail: hulijun@lsec.cc.ac.cn).

  • 中图分类号: O354;O241.82

A Genuinely Multidimensional Riemann Solver Based on the TV Splitting

Funds: The National Basic Research Program of China(973 Program)(2010CB731505); The National Natural Science Foundation of China(11321061)
  • 摘要: 给出了一种真正多维的HLL Riemann解法器.采用TV(Toro-Vázquez)分裂将通量分裂成对流通量和压力通量,其中对流通量的计算采用类似于AUSM格式的迎风方法,压力通量的计算采用波速基于压力系统特征值的HLL格式,并将HLL格式耗散项中的密度差用压力差代替,来克服传统的HLL格式不能分辨接触间断的缺点.为了实现数值格式真正多维的特性,分别计算网格界面中点和角点上的数值通量,并且采用Simpson公式加权中点和角点上的数值通量来得到网格界面上的数值通量.采用基于SDWLS(solution dependent weighted least squares)梯度的线性重构来获得空间的二阶精度,时间离散采用二阶Runge-Kutta格式.数值实验表明,相比于传统的一维HLL格式,该文的真正多维HLL格式具有能够分辨接触间断,消除慢行激波波后振荡以及更大的时间步长等优点.并且,与其他能够分辨接触间断的格式(例如HLLC格式)不同的是,真正多维的HLL格式在计算二维问题时不会出现数值激波不稳定现象.
  • [1] Roe P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics,1981,43(2): 357-372.
    [2] Harten A, Lax P D, van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws[J]. SIAM Review,1983,25(1): 35-61.
    [3] Toro E F, Spruce M, Speares W. Restoration of the contact surface in the HLL-Riemann solver[J]. Shock Waves,1994,4(1): 25-34.
    [4] Quirk J J. A contribution to the great Riemann solver debate[J]. International Journal for Numerical Methods in Fluids,1994,18(6): 555-574.
    [5] LIOU Meng-sing. Mass flux schemes and connection to shock instability[J]. Journal of Computational Physics,2000,160(2): 623-648.
    [6] Pandolfi M, d’Ambrosio D. Numerical instabilities in upwind methods: analysis and cures for the “Carbuncle” phenomenon[J]. Journal of Computational Physics,2001,166(2): 271-301.
    [7] Kim S S, Kim C, Rho O H, et al. Cures for the shock instability: development of a shock-stable Roe scheme[J]. Journal of Computational Physics,2003,185(2): 342-374.
    [8] Chauvat Y, Moschetta J M, Gressier J. Shock wave numerical structure and the carbuncle phenomenon[J]. International Journal for Numerical Methods in Fluids,2005,47(8/9): 903-909.
    [9] Kim S D, Lee B J, Lee H J, et al. Robust HLLC Riemann solver with weighted average flux scheme for strong shock[J]. Journal of Computational Physics,2009,228(20): 7634-7642.
    [10] Steger J L, Warming R F. Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods[J]. Journal of Computational Physics,1981,40(2): 263-293.
    [11] van Leer B. Flux vector splitting for the Euler equations[C]//8th International Conference on Numerical Methods in Fluid Dynamics.Berlin, Heidelberg: Springer-Verlag, 1982: 507-512.
    [12] Anderson W K, Thomas J L, van Leer B. Comparison of finite volume flux vector splittings for the Euler equations[J]. AIAA Journal,1986,24(9): 1453-1460.
    [13] Anderson W K, Thomas J L, Rumsey C L. Extension and application of flux-vector splitting to calculations on dynamic meshes[J]. AIAA Journal,1989,27(6): 673-674.
    [14] LIOU Meng-sing, Steffen Jr C J. A new flux splitting scheme[J]. Journal of Computational Physics,1993,107(1): 23-39.
    [15] LIOU Meng-sing. A sequel to AUSM: AUSM+[J]. Journal of Computational Physics,1996,129(2): 364-382.
    [16] LIOU Meng-sing. Recent progress and applications of AUSM+[C]// Bruneau C H, ed. Sixteenth International Conference on Numerical Methods in Fluid Dynamics.Berlin: Springer-Verlag, 1998: 302-307.
    [17] LIOU Meng-sing. A sequel to AUSM, part II: AUSM+-up for all speeds[J]. Journal of Computational Physics,2006,214(1): 137-170.
    [18] Zha G C, Bilgen E. Numerical solutions of Euler equations by using a new flux vector splitting scheme[J]. International Journal for Numerical Methods in Fluids,1993,17(2): 115-144.
    [19] Toro E F, Vázquez-Cendón M E. Flux splitting schemes for the Euler equations[J]. Computers & Fluids,2012,70: 1-12.
    [20] Collela P. Multidimensional upwind methods for hyperbolic conservation laws[J]. Journal of Computational Physics,1990,87(1): 171-200.
    [21] Brio M, Zakharian A R, Webb G M. Two-dimensional Riemann solver for Euler equations of gas dynamics[J]. Journal of Computational Physics,2001,167(1): 177-195.
    [22] LeVeque R J. Wave propagation algorithms for multidimensional hyperbolic systems[J].Journal of Computational Physics,1997,131(2): 327-353.
    [23] Fey M. Multidimensional upwinding—part I: the method of transport for solving the Euler equations[J]. Journal of Computational Physics,1998,143(1): 159-180.
    [24] Fey M. Multidimensional upwinding—part II: decomposition of the Euler equations into advection equations[J]. Journal of Computational Physics,1998,143(1): 181-203.
    [25] Wendroff B. A two-dimensional HLLE Riemann solver and associated Godunov-type difference scheme for gas dynamics[J]. Computers & Mathematics With Applications,1999,38(11/12): 175-185.
    [26] Balsara D S. Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows[J]. Journal of Computational Physics,2010,229(6): 1970-1993.
    [27] Balsara D S. A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows[J]. Journal of Computational Physics,2012,231(22): 7476-7503.
    [28] Balsara D S. Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows[J]. Journal of Computational Physics,2015,295: 1-23.
    [29] Capdeville G. A high-order multi-dimensional HLL Riemann solver for non-linear Euler equations[J]. Journal of Computational Physics,2011,230(8): 2915-2951.
    [30] Vides J, Nkonga B, Audit E. A simple two-dimensional extension of the HLL Riemann solver for hyperbolic systems of conservation laws[J]. Journal of Computational Physics,2015,280: 643-675.
    [31] Mandal J C, Sharma V. A genuinely multidimensional convective pressure flux split Riemann solver for Euler equations[J]. Journal of Computational Physics,2015,297: 669-688.
    [32] Mandal J C, Panwar V. Robust HLL-type Riemann solver capable of resolving contact discontinuity[J]. Computers & Fluids,2012,63: 148-164.
    [33] Gottlieb S. On high order strong stability preserving Runge-Kutta and multi step time discretizations[J]. Journal of Scientific Computing,2005,25(1): 105-128.
    [34] Mandal J C, Arvind N. High resolution schemes for genuinely two-dimensional HLLE Riemann solver[J]. Progress in Computational Fluid Dynamics,2014,14(4): 205-220.
    [35] JIANG Guang-shan, SHU Chi-wang. Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1): 202-228.
    [36] Toro E F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction [M]. 3rd ed. Berlin: Springer, 2009.
    [37] Woodward P, Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks[J]. Journal of Computational Physics,1984,54(1): 115-173.
    [38] San O, Kara K. Numerical assessments of high-order accurate shock capturing schemes: Kelvin-Helmholtz type vortical structures in high-resolutions[J]. Computer & Fluid,2014,89: 254-276.
    [39] Schulz-Rinne C W, Collins J P, Glaz H M. Numerical solution of the Riemann problem for two-dimensional gas dynamics[J]. SIAM Journal of Scientific Computing,1993,14(6): 1394-1414.
    [40] XU Kun. Gas-kinetic schemes for unsteady compressible flow simulations[R]. Von Karman Institute for Fluid Dynamics Lecture Series, 1998: 1-10.
    [41] Dumbser M, Moschetta J M, Gressier J. A matrix stability analysis of the carbuncle phenomenon[J]. Journal of Computational Physics,2004,197(2): 647-670.
    [42] Moschetta J M, Gressier J, Robinet J C, et al. The carbuncle phenomenon: a genuine Euler instability?[M]//Toro E F, ed. Godunov Methods: Theory and Applications.New York: Kluwer Academic/Plenum Publisher, 1995: 639-645.
    [43] WU Hao, SHEN Long-jun, SHEN Zhi-jun. A hybrid numerical method to cure numerical shock instability[J]. Communications in Computational Physics,2010,8(5): 1264-1271.
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出版历程
  • 收稿日期:  2016-07-04
  • 修回日期:  2016-08-11
  • 刊出日期:  2017-03-15

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