Yao Yuan, Zhang Xiaolin, Liu Rongke, et al. Algorithm for color image coding based on wavelet zerotree[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(04): 481-484. (in Chinese)
Citation: XU Weizheng, KONG Xiangshao, ZHENG Cheng, et al. An improved method for third-order WENO-Z scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863(in Chinese)

An improved method for third-order WENO-Z scheme

doi: 10.13700/j.bh.1001-5965.2016.0863
Funds:

National Defense Basic Research Program B1420133057

National Natural Science Foundation of China 51409202

the Fundamental Research Funds for the Central Universities 2016-YB-016

More Information
  • Corresponding author: KONG Xiangshao, E-mail:kongxs@whut.edu.cn
  • Received Date: 10 Nov 2016
  • Accepted Date: 20 Jan 2017
  • Publish Date: 20 Dec 2017
  • 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.

     

  • [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.
    [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.

    WANG 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).
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