RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD APPLIED TO SHALLOW WATER EQUATIONS

被引：0
作者：
Poussel, C. [1 ]
Ersoy, M. [1 ]
Golay, F. [1 ]
Mannes, Y. [1 ]
机构：
[1] Univ Toulon & Var, IMATH, EA 2137, F-83957 La Garde, France
来源：
TOPICAL PROBLEMS OF FLUID MECHANICS 2023 | 2023年
关键词：
Discontinuous Galerkin method; Shallow Water Equations; Moment limiter; Non-conformal mesh; FINITE-ELEMENT-METHOD; CONSERVATION-LAWS; TOPOGRAPHY; DERIVATION;
D O I：
10.14311/TPFM.2023.021
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
This work is devoted to the numerical simulation of Shallow Water Equations using Runge-Kutta Discontinuous Galerkin methods. Such methods were implemented in the framework of adaptive mesh refinement method using a block-based approach. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Increasing the order of approximation, spurious oscillations appear and are addressed using moment limiters. Finally, the solver is validated with a one-dimensional dam-break problem and its behavior is tested solving a two-dimensional benchmark.
引用
收藏
页码：152 / 159
页数：8
相关论文
共 19 条
  • [1] A discontinuous Galerkin method for two-dimensional flow and transport in shallow water
    Aizinger, V
    Dawson, C
    [J]. ADVANCES IN WATER RESOURCES, 2002, 25 (01) : 67 - 84
  • [2] Numerical investigation of BB-AMR scheme using entropy production as refinement criterion
    Altazin, Thomas
    Ersoy, Mehmet
    Golay, Frederic
    Sous, Damien
    Yushchenko, Lyudmyla
    [J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, 2016, 30 (03) : 256 - 271
  • [3] Space-time discontinuous Galerkin finite element method for shallow water flows
    Ambati, V. R.
    Bokhove, O.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 204 (02) : 452 - 462
  • [4] An adaptive strategy for discontinuous Galerkin simulations of Richards' equation: Application to multi-materials dam wetting
    Clement, Jean-Baptiste
    Golay, Frederic
    Ersoy, Mehmet
    Sous, Damien
    [J]. ADVANCES IN WATER RESOURCES, 2021, 151
  • [5] Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    Cockburn, Bernardo
    Shu, Chi-Wang
    [J]. Journal of Scientific Computing, 2001, 16 (03) : 173 - 261
  • [6] TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .2. GENERAL FRAMEWORK
    COCKBURN, B
    SHU, CW
    [J]. MATHEMATICS OF COMPUTATION, 1989, 52 (186) : 411 - 435
  • [7] TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .3. ONE-DIMENSIONAL SYSTEMS
    COCKBURN, B
    LIN, SY
    SHU, CW
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 84 (01) : 90 - 113
  • [8] De Saint-Venant A.J.C.B., 1871, Theorie Du Mouvement Non Permanent Des Eaux, Avec Application Aux Crues Des Rivieres et a l'introduction Des Marees Dans Leur Lit. Comptes Rendus Hebdomadaires Des Seances de l'Academie Des Sciences
  • [9] SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies
    Delestre, Olivier
    Lucas, Carine
    Ksinant, Pierre-Antoine
    Darboux, Frederic
    Laguerre, Christian
    Vo, T. -N. -Tuoi
    James, Francois
    Cordier, Stephane
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2013, 72 (03) : 269 - 300
  • [10] Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods
    Delis, AI
    Katsaounis, T
    [J]. APPLIED MATHEMATICAL MODELLING, 2005, 29 (08) : 754 - 783
12