-
摘要:
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。在三阶WENO-Z格式（WENO-Z3）基础上，通过构造不同形式的全局光滑因子得到WENO-Z3N1、WENO-Z3N2、WENO-Z3N3格式。选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用等经典算例，考察了3种格式（WENO-Z3N1、WENO-Z3N2、WENO-Z3N3）的计算性能。根据泰勒级数展开，理论推导给出3种格式的精度分析。通过探讨各格式理论精度与实际计算精度之间的关系得到如下结论：3种格式在连续解非极值点处的理论精度对实际计算性能起决定性的作用，并通过双马赫反射问题进一步验证该结论的可靠性。本文的研究给出一种三阶WENO-Z格式的改进方法，合理构造全局光滑因子使得格式在连续解非极值点处满足设计精度的要求。
-
关键词:
- 三阶WENO-Z格式 /
- 全局光滑因子 /
- 精度分析 /
- 低耗散 /
- 高分辨率
Abstract:High resolution shock capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. WENO-Z3N1, WENO-Z3N2 and WENO-Z3N3 schemes were constructed through different global smoothness indicators based on the third-order WENO-Z scheme (WENO-Z3 scheme). Several classical examples such as sod problem, interacting blast wave and shock entropy wave interaction were simulated to investigate the computing performance of the three schemes (WENO-Z3N1, WENO-Z3N2, WENO-Z3N3). Precision of the three schemes was analyzed theoretically according to Taylor series expansion. It is concluded that theoretical precision of the three schemes at non-critical points plays the important role in the actual computing performance after discussion on the relationship between the theoretical precision and actual calculation accuracy. Double Mach reflection problem was conducted to further verify the reliability of the above conclusion. The research in the present paper gives an improved method for third-order WENO-Z scheme:global smoothness indicators should be reasonably constructed to make scheme satisfy the requirement of design precision at non-critical points in the smooth flow fields.
-
图 1 Sod激波管计算结束后密度曲线局部放大图
Figure 1. Partial enlarged details of density curves after calculation for Sod shock tube
图 2 双爆轰波碰撞计算结束后密度曲线局部放大图
Figure 2. Partial enlarged details of density curves after calculation for interacting blast waves
图 3 激波与熵波相互作用计算结束后密度曲线局部放大图
Figure 3. Partial enlarged details of density curves after calculation for shock entropy wave interaction
-
[1] LIU X D, OSHER S, CHAN T.Weighted essentially non-oscillatory schemes[J].Journal of Computational Physics, 1994, 115(1):200-212. doi: 10.1006/jcph.1994.1187 [2] JIANG G S, SHU C W.Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics, 1996, 126(1):202-228. doi: 10.1006/jcph.1996.0130 [3] SHU C W.Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws[M].Berlin:Springer, 1998:325-432. [4] SHU C W.High order weighted essentially nonoscillatory schemes for convection dominated problems[J].SIAM Review, 2009, 51(1):82-126. doi: 10.1137/070679065 [5] 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. doi: 10.1016/j.jcp.2005.01.023 [6] 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. doi: 10.1016/j.jcp.2007.11.038 [7] YAMALEEV N K, CARPENTER M H.Third-order energy stable WENO scheme[J].Journal of Computational Physics, 2009, 228(8):3025-3047. doi: 10.1016/j.jcp.2009.01.011 [8] WU X, ZHAO Y.A high-resolution hybrid scheme for hyperbolic conservation laws[J].International Journal for Numerical Methods in Fluids, 2015, 78(3):162-187. doi: 10.1002/FLD.v78.3 [9] WU X, LIANG J, ZHAO Y.A new smoothness indicator for third-order WENO scheme[J].International Journal for Numerical Methods in Fluids, 2015, 81(7):451-459. doi: 10.1002/fld.4194/full [10] HU X Y, WANG Q, ADAMS N A.An adaptive central-upwind weighted essentially non-oscillatory scheme[J].Journal of Computational Physics, 2010, 229(23):8952-8965. doi: 10.1016/j.jcp.2010.08.019 [11] ACKER F, BORGES R B D R, COSTA B.An improved WENO-Z scheme[J].Journal of Computational Physics, 2016, 313:726-753. doi: 10.1016/j.jcp.2016.01.038 [12] 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. https://www.sciencedirect.com/science/article/pii/S0021999113003501 [13] SHU C W, OSHER S.Efficient implementation of essentially non-oscillatory shock-capturing schemes[J].Journal of Computational Physics, 1988, 77(2):439-471. doi: 10.1016/0021-9991(88)90177-5 [14] SHI J, ZHANG Y T, SHU C W.Resolution of high order WENO schemes for complicated flow structures[J].Journal of Computational Physics, 2003, 186(2):690-696. doi: 10.1016/S0021-9991(03)00094-9 [15] 吴晓帅, 赵玉新. 低耗散中心-WENO混合格式[C]//中国计算力学大会2014暨钱令希计算力学奖颁奖大会论文集. 北京: 中国计算力学大会, 2014: 890-895.WU X S, ZHAO Y X.Low-dissipation hybrid central-WENO scheme[C]//Proceedings of Conference on Computational Mechanics in China 2014 and Qian Lingxi Computational Mechanics Awards Assembly.Beijing:China Computational Mechanics Conference, 2014:890-895(in Chinese). [16] 王来, 吴颂平.无自由参数型混合格式[J].北京航空航天大学学报, 2015, 41(2):318-322. http://bhxb.buaa.edu.cn/CN/abstract/abstract13166.shtmlWANG L, WU S P.Hybrid finite difference schemes without parameters[J].Journal of Beijign University of Aeronautics and Astronautics, 2015, 41(2):318-322(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract13166.shtml -
下载:
点击查看大图
计量
- 文章访问数: 692
- HTML全文浏览量: 105
- PDF下载量: 351
- 被引次数: 0
