# 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 (2012)

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

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topCastro 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 47.1 (2012): 1-32. <http://eudml.org/doc/222167>.

@article{CastroDíaz2012,

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},

keywords = {Well-balanced; finite volume method; path-conservative; simple Riemann solver; HLLC; well-balanced},

language = {eng},

month = {7},

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/222167},

volume = {47},

year = {2012},

}

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

DA - 2012/7//

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; well-balanced

UR - http://eudml.org/doc/222167

ER -

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