EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一种在网格内部捕捉间断的Walsh函数有限体积方法

任炯 王刚

任炯, 王刚. 一种在网格内部捕捉间断的Walsh函数有限体积方法[J]. 力学学报, 2021, 53(3): 773-788. doi: 10.6052/0459-1879-20-253
引用本文: 任炯, 王刚. 一种在网格内部捕捉间断的Walsh函数有限体积方法[J]. 力学学报, 2021, 53(3): 773-788. doi: 10.6052/0459-1879-20-253
Ren Jiong, Wang Gang. A FINITE VOLUME METHOD WITH WALSH BASIS FUNCTIONS TO CAPTURE DISCONTINUITY INSIDE GRID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 773-788. doi: 10.6052/0459-1879-20-253
Citation: Ren Jiong, Wang Gang. A FINITE VOLUME METHOD WITH WALSH BASIS FUNCTIONS TO CAPTURE DISCONTINUITY INSIDE GRID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 773-788. doi: 10.6052/0459-1879-20-253

一种在网格内部捕捉间断的Walsh函数有限体积方法

doi: 10.6052/0459-1879-20-253
基金项目: 1) 国家自然科学基金(11772265);国家自然科学基金(92052109);国家数值风洞工程基础课题(NNW2019ZT7-B22)
详细信息
    作者简介:

    2) 王刚, 教授, 主要研究方向: 计算流体力学. E-mail: wanggang@nwpu.edu.cn

    通讯作者:

    王刚

  • 中图分类号: V211.3

A FINITE VOLUME METHOD WITH WALSH BASIS FUNCTIONS TO CAPTURE DISCONTINUITY INSIDE GRID

  • 摘要: 传统有限体积或有限元方法假定流动变量在单元内连续, 间断仅限于控制体的交界面上, 因此它们无法在控制体内部捕捉间断. 本文摒弃控制体内流动变量连续的假设, 将自身具有间断特点的Walsh基函数应用于有限体积方法, 把控制体内的流场变量表示成间断基函数的组合形式. 按照Walsh基函数在控制体内引入的间断数目和位置, 将控制体单元虚分为若干个分片连续的子单元, 并将Walsh基函数级数表征的守恒型控制方程在每个子单元上进行数值积分和离散求解.相对于传统有限体积方法, 这种利用Walsh基函数构造的新型有限体积方法能够以一定的比例减小数值误差, 提高分辨率, 并可实现控制体单元内部的间断捕捉, 本文将其命名为Walsh函数有限体积方法. 该方法在子单元尺度上仅具有一阶计算精度, 为进一步提高对光滑解的分辨率, 在每个控制体内利用子单元上的变量平均值进行重构, 提出了子单元尺度上具有的二阶/高阶计算精度的Walsh函数有限体积方法. 最后, 运用新发展的方法求解无黏Burgers方程和Euler方程, 并在相同的计算网格上与传统有限体积方法进行对比计算, 对新方法的计算精度、计算效率、间断捕捉能力和鲁棒性进行了验证.

     

  • [1] Zou DY, Xu CG, Dong HB, et al. A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes. Journal of Computational Physics, 2017,345:866-882
    [2] Bonfiglioli A, Grottadaurea M, Paciorri R, et al. An unstructured, three-dimensional, shock-fitting solver for hypersonic flows. Computers & Fluids, 2013,73:162-174
    [3] Romick CM, Aslam TD. An extension of high-order shock-fitted detonation propagation in explosives. Journal of Computational Physics, 2019,395:765-771
    [4] Romick CM, Aslam TD. High-order shock-fitted detonation propagation in high explosives. Journal of Computational Physics, 2017,332:210-235
    [5] Rawat PS, Zhong XL. On high-order shock-fitting and front-tracking schemes for numerical simulation of shock-- disturbance interactions. Journal of Computational Physics, 2010,229(19):6744-6780
    [6] Toro EF. Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd ed. Springer-Verlag, 1999
    [7] LeVeque RJ. Numerical Methods for Conservation Laws. Birkhauser-Verlag, 1992
    [8] Tannehill JC, Anderson DA, Pletcher RH. Computational Fluid Dynamics and Heat Transfer, 2nd ed. Taylor & Francis, 1997
    [9] 阎超. 计算流体力学方法及应用. 北京: 北京航空航天大学出版社, 2006
    [10] van Leer B. Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method. Journal of Computational Physics, 1997,135:229-248
    [11] Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing Schemes. Journal of Computational Physics, 1988,77(2):439-471
    [12] 李康, 刘娜, 何志伟, 等. 一种基于双界面函数的界面捕捉方法. 力学学报, 2017,49(6):1290-1300

    (Li Kang, Liu Na, He Zhiwei, et al. A new interface capturing method based on double interface function. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(6):1290-1300 (in Chinese))
    [13] 伍鹏革, 倪冰雨, 姜潮. 一种基于Neumann级数的区间有限元方法. 力学学报, 2020,52(5):1431-1442

    (Wu Pengge, Ni Bingyu, Jiang Chao. An interval finite element method based on Neumann series expansion. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(5):1431-1442 (in Chinese))
    [14] 陈林烽. 基于Navier-Stokes方程残差的隐式大涡模拟有限元模型. 力学学报, 2020,52(5):1314-1322

    (Chen Linfeng. A residual-based unresolved-scale finite element modelling for implicit large eddy simulation. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(5):1314-1322 (in Chinese))
    [15] Rong YS, Wei YC. A flux vector splitting scheme for low Mach number flows in preconditioning method. Applied Mathematics and Computation, 2014,242:296-308
    [16] Chen YB, Jiang S, Liu N. HFVS: An arbitrary high order approach based on flux splitting. Journal of Computational Physics, 2016,322:708-722
    [17] Kitamura K, Shima E. Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes. Journal of Computational Physics, 2013,245(1):62-83
    [18] Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics, 1981,43:357-372
    [19] Chen SS, Yan C, Lou S, et al. An improved entropy-consistent Euler flux in low Mach number. Journal of Computational Science, 2018,27:271-283
    [20] Ren J, Wang G, Feng JH, et al. Study of ?ux limiters to minimize the numerical dissipation based on entropy-consistent scheme. Journal of Mechanics, 2018,34(2):135-149
    [21] Ren J, Wang G, Ma BP. Multidimensional extension and application of entropy-consistent scheme for Navier-Stokes equations on unstructured grids. AIAA Paper 2017-4403, 2017
    [22] Ren J, Wang G, Ma MS. A group of CFL-dependent flux-limiters to control the numerical dissipation in multi-stage unsteady calculation. Journal of Scientific Computing, 2019,81(1):186-216
    [23] Jiang GS, Shu CW. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 1996,126(1):202-228
    [24] 骆信, 吴颂平. 改进的五阶WENO-Z$+$格式. 力学学报, 2019,51(6):1927-1939

    (Luo X, Wu SP. An improved fifth-order WENO-Z$+$ scheme. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1927-1939 (in Chinese))
    [25] Acker F, Borges RBDR, Costa B. An improved WENO-Z scheme. Journal of Computational Physics, 2016,313:726-753
    [26] Jiang ZH, Yan C, Yu J. Efficient methods with higher order interpolation and MOOD strategy for compressible turbulence simulations. Journal of Computational Physics, 2018,371:528-550
    [27] 刘溢浪, 张伟伟, 蒋跃文, 等. 一种基于增量径向基函数插值的流场重构方法. 力学学报, 2014,46(5):694-702

    (Liu Yilang, Zhang Weiwei, Jiang Yuewen, et al. A reconstruction method for finite volume flow field solving based on incremental radial basis functions. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(5):694-702 (in Chinese))
    [28] Bhise AA, Gande NR, Samala R, et al. An efficient hybrid WENO scheme with a problem independent discontinuity locator. International Journal for Numerical Methods in Fluids, 2019,91:1-28
    [29] 李新亮, 傅德薰, 马延文. 8阶群速度控制格式及其应用. 力学学报, 204, 36(1):79-83

    (Li Xinliang, Fu Dexun, Ma Yanwen. Optimized group velocity control scheme. Chinese Journal of Theoretical and Applied Mechanics, 204, 36(1):79-83 (in Chinese))
    [30] Li WN, Ren YX. High order k-exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids. International Journal for Numerical Methods in Fluids, 2012,70(6):742-763
    [31] Wang Q, Ren YX, Li WN. Compact high order finite volume method on unstructured grids II: Extension to two-dimensional Euler equations. Journal of Computational Physics, 2016,314:883-908
    [32] Pan JH, Ren YX, Sun YT. High order sub-cell finite volume schemes for solving hyperbolic conservation laws II: Extension to two-dimensional systems on unstructured grids. Journal of Computational Physics, 2017,338:165-198
    [33] 孔令发, 董义道, 刘伟. 全局方向模板对非结构有限体积梯度与高阶导数重构的影响. 力学学报, 2020,52(5):1334-1349

    (Kong Lingfa, Dong Yidao, Liu Wei. The influence of global-direction stencil on gradient and high-order derivatives of unstructured finite volume methods. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(5):1334-1348 (in Chinese))
    [34] Persson PO, Peraire J. Sub-cell capturing for discontinuous Galerkin methods. AIAA Paper, 2006
    [35] Gnoffo PA. Global series solutions of nonlinear differential equations with shocks using Walsh functions. Journal of Computational Physics, 2014,258(1):650-688
    [36] Gnoffo PA. Solution of nonlinear differential equations with feature detection using fast Walsh transforms. Journal of Computational Physics, 2017,338(1):620-649
    [37] Walsh JL. A closed set of normal orthogonal functions. American Journal of Mathematics, 1923,45(1):5-24
    [38] Andrews HC. Walsh functions in image processing, feature selection and pattern recognition. IEEE Transactions on Electromagnetic Compatibility, 2007, EMC-13(3):26-32
    [39] Gottlieb S, Shu CW, Tadmor E. High order time discretizations with strong stability properties. SIAM Review, 2001,43(1):89-112
    [40] Lax PD, Liu XD. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM Journal on Scientific Computing, 1998,19(2):319-340
    [41] Shi J, Zhang YT, Shu CW. Resolution of high order WENO schemes for complicated flow structures. Journal of Computational Physics, 2003,186(2):690-696
  • 加载中
计量
  • 文章访问数:  598
  • HTML全文浏览量:  90
  • PDF下载量:  155
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-07-19
  • 刊出日期:  2021-03-10

目录

    /

    返回文章
    返回