An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application
-
摘要: 低耗散、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义.在传统三阶WENO格式(WENO-JS3)和三阶WENOZ格式(WENO-Z3)基础上,基于映射函数,给出WENO-M3、WENOMZ3格式.选用Sod激波管、激波与熵波相互作用、双爆轰波碰撞及双Mach(马赫)反射等经典算例,考察上述格式的计算性能.数值结果表明,WENO-MZ3格式相较其他格式具有耗散低、对流场结构分辨率高的特性.为了进一步扩展WENO-MZ3格式的应用范围,采用该格式数值研究封闭方形舱室内柱形高压、高密度气体爆炸波传播过程,波系演化规律以及壁面典型测点压力载荷.数值计算结果表明WENO-MZ3格式能够较好地模拟包含高压比、高密度比的爆炸波且给出数值耗散较小的壁面压力载荷.Abstract: Low-dissipation and high-resolution shock-capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. The WENO-M3 and WENO-MZ3 schemes were proposed with mapping functions based on the classical 3rd-order WENO scheme (WENO-JS3) and the 3rd-order WENO-Z scheme (WENO-Z3). Several classical 1D Riemann problems and double Mach reflection cases were simulated with the above schemes. The simulation results indicate that the WENO-MZ3 scheme has better characteristics of low numerical dissipation and high resolution for the flow features among all the schemes. To expand the application scope of the WENO-MZ3 scheme, the propagation and evolution of blast waves generated by cylindrical high pressure gas in a closed square cabin were investigated. Moreover, 2 typical pressure gauging points on the walls were monitored during the simulation. It is indicated that the WENO-MZ3 scheme is suitable for simulating the evolution of blast waves containing high pressure ratios and high density ratios. The WENO-MZ3 scheme gives lower-dissipation results than the WENO-JS3 scheme for the pressure load on the walls.
-
Key words:
- 3rd-order WENO scheme /
- mapping function /
- high resolution /
- low dissipation /
- explosion
-
[1] LIU Xu-dong, Osher S, Chan T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics,1994,115(1): 200-212. [2] Harten A, Engquist B, Osher S, et al. Uniformly high order accurate essentially non-oscillatory schemes, III[J]. Journal of Computational Physics,1987,71(2): 231-303. [3] JIANG Guang-shan, SHU Chi-wang. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics,1996,126(1): 202-228. [4] Henrick A K, Aslam T D, Powers J M. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points[J]. Journal of Computational Physics,2005,207(2): 542-567. [5] FENG Hui, HU Fu-xing, WANG Rong. A new mapped weighted essentially non-oscillatory scheme[J]. Journal of Scientific Computing,2012,51(2): 449-473. [6] FENG Hui, HUANG Cong, WANG Rong. An improved mapped weighted essentially non-oscillatory scheme[J]. Applied Mathematics & Computation,2014,232(6): 453-468. [7] Borges R, Carmona M, Costa B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics,2008,227(6): 3191-3211. [8] Acker F, Borges R B D R, Costa B. An improved WENO-Z scheme[J]. Journal of Computational Physics,2016,313: 726-753. [9] Zhao S, Lardjane N, Fedioun I. Comparison of improved finite-difference WENO schemes for the implicit large eddy simulation of turbulent non-reacting and reacting high-speed shear flows[J]. Computers & Fluids,2014,95(3): 74-87. [10] Yamaleev N K, Carpenter M H. Third-order energy stable WENO scheme[J]. Journal of Computational Physics,2009,228(8): 3025-3047. [11] WU Xiao-shuai, LIANG Jian-han, ZHAO Yu-xin. A new smoothness indicator for third-order WENO scheme[J]. International Journal for Numerical Methods in Fluids,2016,81: 451-459. [12] WU Xiao-shuai, ZHAO Yu-xin. A high-resolution hybrid scheme for hyperbolic conservation laws[J]. International Journal for Numerical Methods in Fluids,2015,78(3): 162-187. [13] Don W S, Borges R. Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes[J]. Journal of Computational Physics,2013,250(4): 347-372. [14] SHU Chi-wang, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J]. Journal of Computational Physics,1988,77(2): 439-471. [15] Rusanov V V. Calculation of interaction of non-steady shock waves with obstacles[J].Ussr Computational Mathematics & Mathematical Physics,1962. [16] Sod G A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws[J]. Journal of Computational Physics,1978,27(1): 1-31. [17] 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. [18] SHI Jing, ZHANG Yong-tao, SHU Chi-wang. Resolution of high order WENO schemes for complicated flow structures[J]. Journal of Computational Physics,2003,186(2): 690-696. [19] Quirk J J, Karni S. On the dynamics of a shock-bubble interaction[J]. Journal of Fluid Mechanics,1996,318(2): 129-163.
点击查看大图
计量
- 文章访问数: 1028
- HTML全文浏览量: 165
- PDF下载量: 928
- 被引次数: 0