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一种健壮的低耗散通量分裂格式

胡立军 袁礼 翟健

胡立军, 袁礼, 翟健. 一种健壮的低耗散通量分裂格式[J]. 应用数学和力学, 2019, 40(2): 150-166. doi: 10.21656/1000-0887.390132
引用本文: 胡立军, 袁礼, 翟健. 一种健壮的低耗散通量分裂格式[J]. 应用数学和力学, 2019, 40(2): 150-166. doi: 10.21656/1000-0887.390132
HU Lijun, YUAN Li, ZHAI Jian. A Robust and Low-Dissipation Flux Splitting Scheme[J]. Applied Mathematics and Mechanics, 2019, 40(2): 150-166. doi: 10.21656/1000-0887.390132
Citation: HU Lijun, YUAN Li, ZHAI Jian. A Robust and Low-Dissipation Flux Splitting Scheme[J]. Applied Mathematics and Mechanics, 2019, 40(2): 150-166. doi: 10.21656/1000-0887.390132

一种健壮的低耗散通量分裂格式

doi: 10.21656/1000-0887.390132
详细信息
    作者简介:

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

  • 中图分类号: O354;O241.82

A Robust and Low-Dissipation Flux Splitting Scheme

  • 摘要: 随着计算流体力学的快速发展,设计精确、高效并且健壮的数值格式变得尤为重要.通过对3种流行的通量分裂方法(AUSM、Zha-Bilgen和Toro-Vázquez)的对流通量和压力通量进行特征分析,构造了一种简单、低耗散并且健壮的通量分裂格式(命名为R-ZB格式).采用Zha-Bilgen分裂方法将Euler方程的通量分裂成对流通量和压力通量,其中对流通量采用迎风方法来计算,压力通量采用低耗散的HLL格式来计算,从而克服了原始的HLL格式不能精确分辨接触间断的缺点.数值实验表明,该文给出的R-ZB格式不仅保留了原始Zha-Bilgen格式简单高效、能够精确分辨接触间断等优点,而且具有更好的健壮性,在计算二维问题时不会出现数值激波不稳定现象.
  • [1] LIOU M S. Open issues in numerical fluxes: proposed resolutions[C]// 〖STBX〗20th AIAA Computational Fluid Dynamics Conference, Fluid Dynamics and Co-located Conferences,2011. DOI: 10.2514/6.2011-3055.
    [2] QU F, YAN C, YU J, et al. A new flux splitting scheme for the Euler equations[J]. Computers & Fluids,2014,102: 203-214.
    [3] ROE P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics,1981,43(2): 357-372.
    [4] 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.
    [5] 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.
    [6] TORO E F. Riemann Solvers and Numerical Methods for Fluid Dynamics [M]. 3rd ed. Berlin: Springer, 1999.
    [7] 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.
    [8] 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.
    [9] VAN LEER B. Flux vector splitting for the Euler equations[C]// 〖STBX〗8th International Conference on Numerical Methods in Fluid Dynamics . Berlin, Heidelberg: Springer-Verlag, 1982: 507-512.
    [10] 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.
    [11] TORO E F, VZQUEZ-CENDN M E. Flux splitting schemes for the Euler equations[J]. Computers & Fluids,2012,70: 1-12.
    [12] LIOU M S, STEFFEN JR C J. A new flux splitting scheme[J]. Journal of Computational Physics,1993,107(1): 23-39.
    [13] LIOU M S. A sequel to AUSM: AUSM+[J]. Journal of Computational Physics,1996,129(2): 364-382.
    [14] LIOU M S. Recent progress and applications of AUSM+[C]//16th International Conference on Numerical Methods in Fluid Dynamics . Berlin, Germany, 1998.
    [15] LIOU M S. A sequel to AUSM, part II: AUSM+-up for all speeds[J]. Journal of Computational Physics,2006,214(1): 137-170.
    [16] ZHA G C, BILGEN E. Numerical solution of Euler equations by using a new flux vector splitting scheme[J]. International Journal for Numerical Methods in Fluids,1993,17(2): 115-144.
    [17] ZHA G C, SHEN Y, WANG B. An improved low diffusion E-CUSP upwind scheme[J]. Computers & Fluids,2011,48(1): 214-220.
    [18] KAPEN P T, TCHUEN G. An extension of the TV-HLL scheme for multi-dimensional compressible flows[J]. International Journal of Computational Fluid Dynamics,2015,29(3/5): 303-312.
    [19] TORO E F, CASTRO C E, LEE B J. A novel numerical flux for the 3D Euler equations with general equation of state[J]. Journal of Computational Physics,2015,303: 80-94.
    [20] XIE W, LI H, TIAN Z, et al. A low diffusion flux splitting method for inviscid compressible flows[J]. Computers & Fluids,2015,112: 83-93.
    [21] SHIMA E, KITAMURA K. Parameter-free simple low-dissipation AUSM-family scheme for all speeds[J]. AIAA Journal,2011,49(8): 1693-1709.
    [22] MANDAL J C, PANWAR V. Robust HLL-type Riemann solver capable of resolving contact discontinuity[J]. Computers & Fluids,2012,63: 148-164.
    [23] QUIRK J J. A contribution to the great Riemann solver debate[J]. International Journal for Numerical Methods in Fluids,1994,18(6): 555-574.
    [24] HU L J, YUAN L. A robust hybrid HLLC-FORCE scheme for curing numerical shock instability[J]. Applied Mechanics and Materials,2014,577: 749-753.
    [25] WU H, SHEN L J, SHEN Z J. A hybrid numerical method to cure numerical shock instability[J]. Communications in Computational Physics,2010,8: 1264-1271.
    [26] REN Y X. A robust shock-capturing scheme based on rotated Riemann solvers[J]. Computers & Fluids,2003,32(10): 1379-1403.
    [27] 胡立军, 袁礼. 一种治愈强激波数值不稳定性的混合方法[J]. 应用数学和力学, 2015,36(5): 482-493.(HU Lijun, YUAN Li. Analysis of numerical shock instability and a hybrid curing method[J]. Applied Mathematics and Mechanics,2015,36(5): 482-493.(in Chinese))
    [28] SUN M, TAKAYAMA K. An artificially upstream flux vector splitting scheme for the Euler equations[J]. Journal of Computational Physics,2003,189(1): 305-329.
    [29] GOTTLIEB S. On high order strong stability preserving Runge-Kutta and multi step time discretizations[J]. Journal of Scientific Computing,2005,25(1/2): 105-128.
    [30] LI B, YUAN L. Convergence issues in using high-resolution schemes and lower-upper symmetric Gauss-Seidel method for steady shock-induced combustion problems[J]. International Journal for Numerical Methods in Fluid,2013,71(11): 1422-1437.
    [31] JIANG G S, SHU W C. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics,1996,126(1): 202-228.
    [32] 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.
    [33] KITAMURA K, ROE P L, ISMAIL F. Evaluation of Euler fluxes for hypersonic flow computations[J]. AIAA Journal,2009,47(1): 44-53.
    [34] LAX P D, LIU X D. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes[J]. SIAM Journal on Scientific Computing,1998,19(2): 319-340.
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出版历程
  • 收稿日期:  2018-04-25
  • 修回日期:  2018-06-13
  • 刊出日期:  2019-02-01

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