A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport

Manuel Jesús Castro Díaz; Enrique Domingo Fernández-Nieto; Tomás Morales de Luna; Gladys Narbona-Reina; Carlos Parés

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 1, page 1-32
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Castro Díaz, Manuel Jesús, et al. "A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 1-32. <http://eudml.org/doc/273158>.

@article{CastroDíaz2013,
abstract = {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.},
author = {Castro Díaz, Manuel Jesús, Fernández-Nieto, Enrique Domingo, Morales de Luna, Tomás, Narbona-Reina, Gladys, Parés, Carlos},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {well-balanced; finite volume method; path-conservative; simple Riemann solver; HLLC},
language = {eng},
number = {1},
pages = {1-32},
publisher = {EDP-Sciences},
title = {A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport},
url = {http://eudml.org/doc/273158},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 1
SP - 1
EP - 32
AB - 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.
LA - eng
KW - well-balanced; finite volume method; path-conservative; simple Riemann solver; HLLC
UR - http://eudml.org/doc/273158
ER -

References

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