The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity preserving property of the corresponding numerical methods are presented. The numerical results provided by the two HLLC solvers are compared between them and also with those obtained with a Roe-type method in a number of 1d and 2d test problems. This comparison shows that, while the quality of the numerical solutions is comparable, the computational cost of the HLLC solvers is lower, as only some partial information of the eigenstructure of the matrix system is needed.
Mots-clés : well-balanced, finite volume method, path-conservative, simple Riemann solver, HLLC
@article{M2AN_2013__47_1_1_0,
author = {Castro D{\'\i}az, Manuel Jes\'us and Fern\'andez-Nieto, Enrique Domingo and Morales de Luna, Tom\'as and Narbona-Reina, Gladys and Par\'es, Carlos},
title = {A {HLLC} scheme for nonconservative hyperbolic problems. {Application} to turbidity currents with sediment transport},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1--32},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/m2an/2012017},
mrnumber = {2968693},
zbl = {1268.76037},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012017/}
}
TY - JOUR AU - Castro Díaz, Manuel Jesús AU - Fernández-Nieto, Enrique Domingo AU - Morales de Luna, Tomás AU - Narbona-Reina, Gladys AU - Parés, Carlos TI - A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1 EP - 32 VL - 47 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012017/ DO - 10.1051/m2an/2012017 LA - en ID - M2AN_2013__47_1_1_0 ER -
%0 Journal Article %A Castro Díaz, Manuel Jesús %A Fernández-Nieto, Enrique Domingo %A Morales de Luna, Tomás %A Narbona-Reina, Gladys %A Parés, Carlos %T A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1-32 %V 47 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012017/ %R 10.1051/m2an/2012017 %G en %F M2AN_2013__47_1_1_0
Castro Díaz, Manuel Jesús; Fernández-Nieto, Enrique Domingo; Morales de Luna, Tomás; Narbona-Reina, Gladys; Parés, Carlos. A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 1, pp. 1-32. doi : 10.1051/m2an/2012017. http://www.numdam.org/articles/10.1051/m2an/2012017/
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