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高效率的特征型紧致WENO混合格式

骆信 吴颂平

骆信, 吴颂平. 高效率的特征型紧致WENO混合格式[J]. 北京航空航天大学学报, 2020, 46(7): 1379-1386. doi: 10.13700/j.bh.1001-5965.2019.0573
引用本文: 骆信, 吴颂平. 高效率的特征型紧致WENO混合格式[J]. 北京航空航天大学学报, 2020, 46(7): 1379-1386. doi: 10.13700/j.bh.1001-5965.2019.0573
LUO Xin, WU Songping. An efficient characteristic-wise hybrid compact-WENO scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1379-1386. doi: 10.13700/j.bh.1001-5965.2019.0573(in Chinese)
Citation: LUO Xin, WU Songping. An efficient characteristic-wise hybrid compact-WENO scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1379-1386. doi: 10.13700/j.bh.1001-5965.2019.0573(in Chinese)

高效率的特征型紧致WENO混合格式

doi: 10.13700/j.bh.1001-5965.2019.0573
基金项目: 

国家自然科学基金 91530325

详细信息
    作者简介:

    骆信  男, 博士研究生。主要研究方向:计算流体力学

    吴颂平  男, 博士, 教授, 博士生导师。主要研究方向:计算流体力学、有限元方法

    通讯作者:

    吴颂平, E-mail: wusping825@163.com

  • 中图分类号: V211.3

An efficient characteristic-wise hybrid compact-WENO scheme

Funds: 

National Natural Science Foundation of China 91530325

More Information
  • 摘要:

    特征型紧致加权基本无振荡(WENO)混合格式HCW-R结合了迎风紧致格式CS5-P和WENO格式,具有十分优异的分辨率特性。但在求解多维方程组时,HCW-R格式需要求解块状三对角方程组,因而计算代价十分高昂。采用迎风紧致格式CS5-F代替CS5-P,构造了一个新的特征型紧致WENO混合格式HCW-E。由于HCW-E的特殊形式,其可沿迎风方向、由边界处向内推进求解,避免了处理三对角或块状三对角方程组,从而其计算代价与显式格式无异。虽然就分辨率而言,HCW-E稍逊于HCW-R,但前者的计算效率要显著高于后者。因此,当花费相同的计算代价,HCW-E格式可以获得更好的数值结果。一系列求解Euler方程组的数值试验验证了HCW-E的高分辨率特性和相比HCW-R更高的计算效率。HCW-E格式的效率优势在求解高维问题时更为明显。

     

  • 图 1  Lax问题的密度分布曲线

    Figure 1.  Density distribution curves of Lax problem

    图 2  Osher-Shu问题的密度分布曲线

    Figure 2.  Density distribution curves of Osher-Shu problem

    图 3  二维Riemann问题的密度等值线

    Figure 3.  Density contours of 2D Riemann problem

    图 4  双马赫杆区域的密度等值线

    Figure 4.  Density contours at double Mach stems region

    表  1  Lax问题的计算耗时

    Table  1.   Computational time for Lax problem

    格式 WENO-Z(N=100) HCW-R(N=100) HCW-E(N=100) HCW-E(N=120)
    计算耗时/s 2.03 3.20 1.16 1.61
    下载: 导出CSV

    表  2  Osher-Shu问题的计算耗时

    Table  2.   Computational time for Osher-Shu problem

    格式 WENO-Z(N=200) HCW-R(N=200) HCW-E(N=200) HCW-E(N=250)
    计算耗时/s 7.81 17.57 6.36 9.83
    下载: 导出CSV

    表  3  二维Riemann问题的计算耗时

    Table  3.   Computational time for 2D Riemann problem

    格式 WENO-Z(N=400×400) HCW-R(N=400×400) HCW-E(N=400×400) HCW-E(N=600×600)
    计算耗时/s 5188 23439 4473 17347
    下载: 导出CSV

    表  4  双马赫反射问题的计算耗时

    Table  4.   Computational time for double Mach reflection problem

    格式 WENO-Z(N=960×240) HCW-R(N=960×240) HCW-E(N=960×240) HCW-E(N=1 600×400)
    计算耗时/s 7371 31460 6804 28118
    下载: 导出CSV
  • [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] 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
    [4] 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
    [5] ACKER F, BORGES R, COSTA B, et al.An improved WENO-Z scheme[J].Journal of Computational Physics, 2016, 313(1):726-753. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ021479294/
    [6] 骆信, 吴颂平.改进的五阶WENO-Z+格式[J].力学学报, 2019, 51(6):1927-1939. http://d.old.wanfangdata.com.cn/Periodical/lxxb201906029

    LUO X, WU S P.An improved fifth-order WENO-Z+ scheme[J].Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6):1927-1939(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/lxxb201906029
    [7] LELE S K.Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics, 1992, 103(1):16-42. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1301.2885
    [8] PIROZZOLI S.Conservative hybrid compact-WENO schemes for shock-turbulence interaction[J].Journal of Computational Physics, 2002, 178(1):81-117. https://www.sciencedirect.com/science/article/pii/S002199910297021X
    [9] REN Y X, LIU M E, ZHANG H X.A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws[J].Journal of Computational Physics, 2003, 192(2):365-386. https://www.sciencedirect.com/science/article/pii/S002199910300398X
    [10] 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. doi: 10.13700/j.bh.1001-5965.2014.0134

    WANG L, WU S P.Hybrid finite difference schemes without free parameters[J].Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(2):318-322(in Chinese). doi: 10.13700/j.bh.1001-5965.2014.0134
    [11] LI Y S, YAN C, YU J, et al.A new high-accuracy scheme for compressible turbulent flows[J].International Journal of Computational Fluid Dynamics, 2017, 31(9):362-378. doi: 10.1080/10618562.2017.1365844
    [12] PENG J, SHEN Y Q.A novel weighting switch function for uniformly high-order hybrid shock-capturing schemes[J].International Journal for Numerical Methods in Fluids, 2017, 83(9):681-703. doi: 10.1002/fld.4285
    [13] 武从海, 赵宁, 田琳琳.一种改进的紧致WENO混合格式[J].空气动力学学报, 2013, 31(4):477-481. http://d.old.wanfangdata.com.cn/Periodical/kqdlxxb201304012

    WU C H, ZHAO N, TIAN L L.An improved hybrid compact-WENO scheme[J].Acta Aerodynamica Sinica, 2013, 31(4):477-481(inChinese). http://d.old.wanfangdata.com.cn/Periodical/kqdlxxb201304012
    [14] FU D X, MA Y W.A high order accurate difference scheme for complex flow fields[J].Journal of Computational Physics, 1997, 134(1):1-15. doi: 10.1006-jcph.1996.5492/
    [15] LAX P D.Weak solutions of nonlinear hyperbolic equations and their numerical computation[J].Communications on Pure and Applied Mathematics, 1954, 7(1):159-193. doi: 10.1002/cpa.3160070112
    [16] SHU C W, OSHER S.Efficient implementation of essentially non-oscillatory shock-capturing schemes, Ⅱ[J].Journal of Computational Physics, 1989, 83(1):32-78. doi: 10.1007/978-3-642-60543-7_14
    [17] 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. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0c4383af1961db475fda9b4efdf679b4
    [18] 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. doi: 10.1016-0021-9991(84)90142-6/
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出版历程
  • 收稿日期:  2019-11-10
  • 录用日期:  2020-02-02
  • 刊出日期:  2020-07-20

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