ADER schemes and high order coupling on networks of hyperbolic conservation laws

被引：23
作者：
Borsche, Raul [1 ]
Kall, Jochen [1 ]
机构：
[1] TU Kaiserslautern, D-67663 Kaiserslautern, Germany
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 273卷
关键词：
ADER; Network; Hyperbolic conservation law; WENO; Generalized Riemann problem; Coupling; ESSENTIALLY NONOSCILLATORY SCHEMES; FINITE-VOLUME SCHEMES; RIEMANN PROBLEM; EFFICIENT IMPLEMENTATION; UNSTRUCTURED MESHES; GAS NETWORKS; BALANCE LAWS; P-SYSTEM; SIMULATIONS; EQUATIONS;
D O I：
10.1016/j.jcp.2014.05.042
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling conditions. Several numerical examples confirm the benefits of a high order coupling procedure for high order accuracy and stable shock capturing. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：658 / 670
页数：13
相关论文
共 40 条
  • [1] ADAPTIVE ADER METHODS USING KERNEL-BASED POLYHARMONIC SPLINE WENO RECONSTRUCTION
    Aboiyar, Terhemen
    Georgoulis, Emmanuil H.
    Iske, Armin
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (06) : 3251 - 3277
  • [2] Alastruey J, 2008, COMMUN COMPUT PHYS, V4, P317
  • [3] [Anonymous], 2006, AIMS SER APPL MATH
  • [4] Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes - Speed comparisons with Runge-Kutta methods
    Balsara, Dinshaw S.
    Meyer, Chad
    Dumbser, Michael
    Du, Huijing
    Xu, Zhiliang
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 235 : 934 - 969
  • [5] Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics
    Balsara, Dinshaw S.
    Rumpf, Tobias
    Dumbser, Michael
    Munz, Claus-Dieter
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (07) : 2480 - 2516
  • [6] Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
    Balsara, DS
    Shu, CW
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 160 (02) : 405 - 452
  • [7] Coupling conditions for gas networks governed by the isothermal Euler equations
    Banda, Mapundi K.
    Herty, Michael
    Klar, Axel
    [J]. NETWORKS AND HETEROGENEOUS MEDIA, 2006, 1 (02) : 295 - 314
  • [8] Borsche R., 2011, THESIS U KAISERSLAUT
  • [9] On the coupling of systems of hyperbolic conservation laws with ordinary differential equations
    Borsche, Raul
    Colombo, Rinaldo M.
    Garavello, Mauro
    [J]. NONLINEARITY, 2010, 23 (11) : 2749 - 2770
  • [10] Numerical algorithms for simulations of a traffic model on road networks
    Bretti, G.
    Natalini, R.
    Piccoli, B.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 210 (1-2) : 71 - 77
1234