基于AUSM分裂的二维通量分裂格式

胡立军; 吴世枫; 翟健

doi:10.21656/1000-0887.400264

基于AUSM分裂的二维通量分裂格式

doi: 10.21656/1000-0887.400264

¹衡阳师范学院数学与统计学院, 湖南衡阳 421002;²广东技术师范大学数学与系统科学学院, 广州 510665; ³曙光信息产业(北京)有限公司, 北京 100193

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
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出版历程
- 收稿日期: 2019-09-06
- 修回日期: 2019-11-02
- 刊出日期: 2020-06-01

A 2D Flux Splitting Scheme Based on the AUSM Splitting

¹College of Mathematics and Statistics, Hengyang Normal University,Hengyang, Hunan 421002, P.R.China;²School of Mathematics and System Sciences, Guangdong Polytechnic Normal University, Guangzhou 510665, P.R.China;³Dawning Information Industry Co., Ltd., Beijing 100193, P.R.China)

摘要

摘要: 基于对流迎风分裂思想构造的AUSM类格式具有简单、高效、分辨率高等优点,在计算流体力学中得到了广泛的应用.传统的AUSM类格式在计算界面数值通量时只考虑网格界面法向的波系,忽略了网格界面横向波系的影响.使用Liou-Steffen通量分裂方法将二维Euler方程的通量分裂成对流通量和压力通量,采用AUSM格式来分别计算对流数值通量和压力数值通量.通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的AUSM通量分裂格式.在计算一维算例时,该格式保留了精确捕捉激波和接触间断的优点.在计算二维算例时,该格式不仅具有更高的分辨率而且表现出更好的鲁棒性,可以消除强激波波后的不稳定现象.此外,在多维问题的数值模拟中,该格式大大地提高了稳定性CFL数,具有更高的计算效率.因此,它是一种精确、高效并且强鲁棒性的数值方法.
- 可压缩流 /
- Liou-Steffen分裂 /
- AUSM格式 /
- GT-AUSM格式 /
- 鲁棒性
Abstract: The AUSM-type schemes based on the advection upstream splitting method have the advantages of simpleness, high efficiency and high resolution, and are widely applied in computational fluid dynamics. The traditional AUSM-type schemes only consider the normal waves to the cell interface while ignoring the influence of tangential waves to the interface in the computation of the interfacial numerical flux. The flux of 2D Euler equations was split into the convective flux and the pressure flux by means of the AUSM splitting method, and they were both computed with the modified AUSM scheme. In the solution of the numerical flux at the corners where the influence of tangential waves was considered, a genuinely 2D AUSM flux splitting scheme was constructed. In the computation of 1D numerical examples, the proposed scheme keeps the merits of capturing shocks and contact discontinuities accurately. In the computation of the 2D numerical examples, the scheme has higher resolution and better robustness, while eliminating the instability behind the strong shock waves. In addition, with the scheme the stable CFL number greatly improves and the computation efficiency rises in the simulation of multidimensional problems. Therefore, the proposed scheme makes an accurate, efficient and robust numerical method.
- compressible flow /
- Liou-Steffen splitting /
- AUSM scheme /
- GT-AUSM scheme /
- robustness

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参考文献(29)

[1]	ROE P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics,1981,43(2): 357-372.
[2]	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.
[3]	STEGER J L, WARMING R F. Flux vector splitting of the inviscid gas dynamic equations with application to finite-difference methods[J]. Journal of Computational Physics,1981,40(2): 263-293.
[4]	VAN LEER B. Flux-vector splitting for the Euler equation[C]//8th International Conference on Numerical Methods in Fluid Dynamics . Berlin, Heidelberg: Springer-Verlag, 1982.
[5]	TORO E F, VZQUEZ-CENDN M E. Flux splitting schemes for the Euler equations[J]. Computers & Fluids,2012,70: 1-12.
[6]	LIOU M S, JR STEFFEN C J. A new flux splitting scheme[J]. Journal of Computational Physics,1993,107(1): 23-39.
[7]	LIOU M S. A sequel to AUSM: AUSM⁺[J]. Journal of Computational Physics,1996,129(2): 364-382.
[8]	KIM K H, LEE J H, RHO O H. An improvement of AUSM schemes by introducing the pressure-based weight functions[J]. Computers and Fluids,1998,27(3): 311-346.
[9]	KIM K H, LEE J H, RHO O H. Methods for the accurate computations of hypersonic flows Ⅰ: AUSMPW+ scheme[J]. Journal of Computational Physics,2001,174(1): 38-80.
[10]	LIOU M S. A sequel to AUSM, part Ⅱ: AUSM⁺-up for all speeds[J]. Journal of Computational Physics,2006,214(1): 137-170.
[11]	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.(HU Lijun, YUAN Li. A genuinely multidimensional Riemann solver based on the TV splitting[J]. Applied Mathematics and Mechanics,2017,38(3): 243-264.(in Chinese))
[12]	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.
[13]	RUMSEY C B, VAN LEER B, ROE P L. A multidimensional flux function with application to the Euler and Navier-Stokes equations[J]. Journal of Computational Physics,1993,105(2): 306-323.
[14]	COLLELA P. Multidimensional upwind methods for hyperbolic conservation laws[J]. Journal of Computational Physics,1990,87(1): 171-200.
[15]	LEVEQUE R J. Wave propagation algorithms for multidimensional hyperbolic systems[J]. Journal of Computational Physics,1997,131(2): 327-353.
[16]	SALTZMAN J. An unsplit 3D upwind method for hyperbolic conservation laws[J]. Journal of Computational Physics,1994,115(1): 153-168.
[17]	ROE P L. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics[J]. Journal of Computational Physics,1986,63(2): 458-476.
[18]	FEY M. Multidimensional upwinding, part Ⅰ: the method of transport for solving the Euler equations[J]. Journal of Computational Physics,1998,143: 159-180.
[19]	FEY M. Multidimensional upwinding, part Ⅱ: decomposition of the Euler equations into advection equations[J]. Journal of Computational Physics,1998,143: 181-203.
[20]	WENDROFF B. A two-dimensional HLLE Riemann solver and associated Godunov-type difference scheme for gas dynamics[J]. Computers & Mathematics With Applications,1999,38(1): 175-185.
[21]	BALSARA D S. Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows[J]. Journal of Computational Physics,2010,229(6): 1970-1993.
[22]	BALSARA D S. A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and MHD flows[J]. Journal of Computational Physics,2012,231(22): 7476-7503.
[23]	BALSARA D S. Multidimensional Riemann problem with self-similar internal structure, part Ⅰ: application to hyperbolic conservation laws on structured meshes[J]. Journal of Computational Physics,2014,277: 163-200.
[24]	DUMBSER M, BALSARA D S. A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems[J]. Journal of Computational Physics,2016,304: 275-319.
[25]	BALSARA D S, NKONGA B. Multidimensional Riemann problem with self-similar internal structure, part Ⅲ: a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems[J]. Journal of Computational Physics,2017,346: 25-48.
[26]	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.
[27]	QU F, SUN D, BAI J Q, et al. A genuinely two-dimensional Riemann solver for compressible flows in curvilinear coordinates[J]. Journal of Computational Physics,2019,386: 47-63.
[28]	胡立军, 袁礼. 一种基于AUSM分裂的真正多维HLL格式[J]. 气体物理, 2016,1(6): 22-35.(HU Lijun, YUAN Li. A genuinely multidimensional HLL Riemann solver based on AUSM splitting[J]. Physics of Gases,2016,1(6): 22-35.(in Chinese))
[29]	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.