Volume 41 Issue 8
Aug.  2026
Turn off MathJax
Article Contents
Zhang Tianyi, Hao Shixi, Zhao Ming, et al. Coupled two-phase flow solver based on entropy viscosity within DGSEM framework[J]. Journal of Aerospace Power, 2026, 41(8):20250022 doi: 10.13224/j.cnki.jasp.20250022
Citation: Zhang Tianyi, Hao Shixi, Zhao Ming, et al. Coupled two-phase flow solver based on entropy viscosity within DGSEM framework[J]. Journal of Aerospace Power, 2026, 41(8):20250022 doi: 10.13224/j.cnki.jasp.20250022

Coupled two-phase flow solver based on entropy viscosity within DGSEM framework

doi: 10.13224/j.cnki.jasp.20250022
  • Received Date: 2025-01-14
    Available Online: 2026-05-11
  • To deal with the issues of accuracy degradation and Gibbs phenomena caused by discontinuities such as shock waves, contact discontinuities, and free interfaces in the numerical simulation of compressible two-phase flows, a coupled solution method was developed based on the discontinuous Galerkin spectral element method (DGSEM) framework. To address the issue of discontinuities in single phase, an entropy viscosity model that can automatically distinguish shocks from contact discontinuities and adaptively add artificial viscosity was introduced. The solution method was also coupled with the level-set method, which was discretized by the DGSEM framework and combined with the ghost fluid approach to accurately track the material interface and solve the flow field simultaneously. Numerical results showed that this method can achieve the designed accuracy in smooth regions. Compared with the variable-step artificial viscosity and the fifth-order weighted essentially non-oscillatory-Z (WENO-Z) scheme, it reduced over-dissipation and obtained more flow-field details. Compared with calculations using the same discontinuous Galerkin method but with dissipative interface models, this method reduced the error at monitoring points by up to 6.4% compared with experimental results when using only one-fourth of the grid density. This proved that the method can effectively improve the accuracy of discontinuity capture and material interface tracking.

     

  • loading
  • [1]
    Reed W H, Hill T R. Triangular mesh methods for the neutron transport equation[R]. Los Alamos, US: Los Alamos Scientific Laboratory, 1973.
    [2]
    Kopriva D A. Implementing spectral methods for partial differential equations: algorithms for scientists and engineers[M]. Dordrecht, Netherlands: Springer Netherlands, 2009.
    [3]
    Bassi F, Franchina N, Ghidoni A, et al. Spectral p-multigrid discontinuous Galerkin solution of the Navier–Stokes equations[J]. International Journal for Numerical Methods in Fluids, 2011, 67(11): 1540-1558. doi: 10.1002/fld.2430
    [4]
    Shu C W. Discontinuous Galerkin methods: general approach and stability[R]. Newport, US: the First International Symposium on Discontinuous Galerkin Methods, 1999.
    [5]
    何志伟, 田保林, 李理, 等. 可压缩多介质流动问题的高精度数值模拟方法[J]. 空气动力学学报, 2021, 39(1): 177-190. He Zhiwei, Tian Baolin, Li Li, et al. High-order numerical simulation method for compressible multi-material flow problems[J]. Acta Aerodynamica Sinica, 2021, 39(1): 177-190. (in Chinese doi: 10.7638/kqdlxxb-2020.0165

    He Zhiwei, Tian Baolin, Li Li, et al. High-order numerical simulation method for compressible multi-material flow problems[J]. Acta Aerodynamica Sinica, 2021, 39(1): 177-190. (in Chinese) doi: 10.7638/kqdlxxb-2020.0165
    [6]
    丁岩, 袁礼. 虚拟流体方法中界面处Riemann问题定义方式的改进[J]. 计算物理, 2010, 27(4): 501-508. Ding Yan, Yuan Li. Improvements on definition of interficial Riemann problem in real ghost fluid method[J]. Chinese Journal of Computational Physics, 2010, 27(4): 501-508. (in Chinese

    Ding Yan, Yuan Li. Improvements on definition of interficial Riemann problem in real ghost fluid method[J]. Chinese Journal of Computational Physics, 2010, 27(4): 501-508. (in Chinese)
    [7]
    Cockburn B, Shu Chiwang. Runge–kutta discontinuous Galerkin methods for convection-dominated problems[J]. Journal of Scientific Computing, 2001, 16(3): 173-261. doi: 10.1023/A:1012873910884
    [8]
    赵雅甜, 阎超, 孙迪, 等. 新型三阶TVD限制器性能分析[J]. 北京航空航天大学学报, 2017, 43(4): 800-805. Zhao Yatian, Yan Chao, Sun Di, et al. Performance analysis of a new-type third-order TVD limiter[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 800-805. (in Chinese

    Zhao Yatian, Yan Chao, Sun Di, et al. Performance analysis of a new-type third-order TVD limiter[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 800-805. (in Chinese)
    [9]
    Cockburn B, Shu Chiwang. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework[J]. Mathematics of Computation, 1989, 52(186): 411. doi: 10.2307/2008474
    [10]
    Krivodonova L. Limiters for high-order discontinuous Galerkin methods[J]. Journal of Computational Physics, 2007, 226(1): 879-896. doi: 10.1016/j.jcp.2007.05.011
    [11]
    Bassi F, Rebay S, Mariotti G, et al. A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows[C]//Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics. Antwerp, Belgium: Technological Institute, 1997: 99-109.
    [12]
    Yu Jian, Hesthaven J S. A study of several artificial viscosity models within the discontinuous Galerkin framework[J]. Communications in Computational Physics, 2025, 27(5): 1309-1343. doi: 10.4208/cicp.oa-2019-0118
    [13]
    Guermond J L, Pasquetti R. Entropy-based nonlinear viscosity for Fourier approximations of conservation laws[J]. Comptes Rendus Mathématique, 2008, 346(13/14): 801-806. doi: 10.1016/j.crma.2008.05.013
    [14]
    Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39(1): 201-225. doi: 10.1016/0021-9991(81)90145-5
    [15]
    Afkhami S, Zaleski S, Bussmann M. A mesh-dependent model for applying dynamic contact angles to VOF simulations[J]. Journal of Computational Physics, 2009, 228(15): 5370-5389. doi: 10.1016/j.jcp.2009.04.027
    [16]
    Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics, 1988, 79(1): 12-49. doi: 10.1016/0021-9991(88)90002-2
    [17]
    Wang Yaguang, Kang Zhan. A velocity field level set method for shape and topology optimization[J]. International Journal for Numerical Methods in Engineering, 2018, 115(11): 1315-1336. doi: 10.1002/nme.5845
    [18]
    Fedkiw R P, Aslam T, Merriman B, et al. A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method)[J]. Journal of Computational Physics, 1999, 152(2): 457-492. doi: 10.1006/jcph.1999.6236
    [19]
    Zingan V, Guermond J L, Morel J, et al. Implementation of the entropy viscosity method with the discontinuous Galerkin method[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 479-490. doi: 10.1016/j.cma.2012.08.018
    [20]
    Zhang Qiang, Shu Chiwang. Error estimates to smooth solutions of runge: kutta discontinuous Galerkin methods for scalar conservation laws[J]. SIAM Journal on Numerical Analysis, 2004, 42(2): 641-666. doi: 10.1137/S0036142902404182
    [21]
    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. doi: 10.1016/0021-9991(78)90023-2
    [22]
    Lax P D, Liu Xudong. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes[J]. SIAM Journal on Scientific Computing, 1998, 19(2): 319-340. doi: 10.1137/S1064827595291819
    [23]
    Tang Shujiang. Improvements of the fifth-order WENO-JS-type scheme with normalized smoothing factor for gas dynamic Euler equations[J]. Applied Numerical Mathematics, 2023, 184: 301-324. doi: 10.1016/j.apnum.2022.10.010
    [24]
    Mikula K, Ševčovič D. A level set method using the signed distance function[J]. Computing and Visualization in Science, 2004, 6(4): 211-223.
    [25]
    Naber J. A Runge-Kutta discontinuous-Galerkin level-set method for unsteady compressible two-fluid flow[D]. Delft, Netherlands: Delft University of Technology, 2005.
    [26]
    Haas J F, Sturtevant B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities[J]. Journal of Fluid Mechanics, 1987, 181: 41-76. doi: 10.1017/S0022112087002003
    [27]
    Quirk J J, Karni S. On the dynamics of a shock-bubble interaction[R]. Hampton, US: NASA Langley Research Center, 1994.
    [28]
    Wackers J, Koren B. Five-equation model for compressible two-fluid flow[R]. MAS-E0414, 2004.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (229) PDF downloads(37) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return