EFFICIENT ENTROPY STABLE GAUSS COLLOCATION METHODS

被引：36
|
作者：
Chan, Jesse [1 ]
Fernandez, David C. Del Rey [2 ]
Carpenter, Mark H. [3 ]
机构：
[1] Rice Univ, Computat & Appl Math, Houston, TX 77005 USA
[2] Univ Toronto, Inst Aerosp Studies, N York, ON M3H 5T6, Canada
[3] NASA, Computat Modeling & Simulat Branch, Langley Res Ctr, Hampton, VA 23681 USA
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2019年 / 41卷 / 05期
关键词：
high order; discontinuous Galerkin; nonlinear conservation laws; entropy; hyperbolic; compressible Euler; DISCONTINUOUS GALERKIN METHODS; NAVIER-STOKES EQUATIONS; BY-PARTS OPERATORS; COMPRESSIBLE EULER; CONSERVATION-LAWS; SCHEMES; ORDER; FORM; DISCRETIZATION; QUADRATURE;
D O I：
10.1137/18M1209234
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semidiscretely entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest that the use of Gauss points significantly improves accuracy on curved meshes.
引用
收藏
页码：A2938 / A2966
页数：29
相关论文
共 50 条
  • [1] Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics
    Rueda-Ramirez, Andres M.
    Hindenlang, Florian J.
    Chan, Jesse
    Gassner, Gregor J.
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2023, 475
  • [2] Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
    Luigi Brugnano
    Gianluca Frasca Caccia
    Felice Iavernaro
    [J]. Numerical Algorithms, 2014, 65 : 633 - 650
  • [3] Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
    Brugnano, Luigi
    Frasca Caccia, Gianluca
    Iavernaro, Felice
    [J]. NUMERICAL ALGORITHMS, 2014, 65 (03) : 633 - 650
  • [4] Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion
    Seyrich, Jonathan
    [J]. PHYSICAL REVIEW D, 2013, 87 (08):
  • [5] Legendre–Gauss collocation methods for ordinary differential equations
    Ben-yu Guo
    Zhong-qing Wang
    [J]. Advances in Computational Mathematics, 2009, 30 : 249 - 280
  • [6] Collocation methods: More efficient procedures for applying collocation
    Herrera, Ismael
    Yates, Robert
    Rubio, Ernesto
    [J]. ADVANCES IN ENGINEERING SOFTWARE, 2007, 38 (10) : 657 - 667
  • [7] Legendre-Gauss collocation methods for ordinary differential equations
    Guo, Ben-yu
    Wang, Zhong-qing
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2009, 30 (03) : 249 - 280
  • [8] Aggregation methods for efficient collocation detection
    Dinu, Anca
    Dinu, Liviu P.
    Sorodoc, Ionut T.
    [J]. LREC 2014 - NINTH INTERNATIONAL CONFERENCE ON LANGUAGE RESOURCES AND EVALUATION, 2014, : 4041 - 4045
  • [9] Efficient implementation of Radau collocation methods
    Brugnano, Luigi
    Iavernaro, Felice
    Magherini, Cecilia
    [J]. APPLIED NUMERICAL MATHEMATICS, 2015, 87 : 100 - 113
  • [10] Stable and convergent unsymmetric meshless collocation methods
    Ling, Leevan
    Schaback, Robert
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (03) : 1097 - 1115
12345