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

Published online by Cambridge University Press:  31 July 2012

Manuel Jesús Castro Díaz ,
Enrique Domingo Fernández-Nieto ,
Tomás Morales de Luna ,
Gladys Narbona-Reina  and
Carlos Parés
Manuel Jesús Castro Díaz
Affiliation:
Dpto. de Análisis Matemático, Facultad de Ciencias, Universidad de Málga, Campus de Teatinos, s/n, 29071 Málaga, Spain. castor@anamat.cie.uma.es; pares@anamat.cie.uma.es
Enrique Domingo Fernández-Nieto
Affiliation:
Dpto. Matemática Aplicada I, ETS Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes No. 2, 41012 Sevilla, Spain; edofer@us.es; gnarbona@us.es
Tomás Morales de Luna
Affiliation:
Dpto. de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071 Córdoba, Spain; tomas.morales@uco.es
Gladys Narbona-Reina
Affiliation:
Dpto. de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071 Córdoba, Spain; tomas.morales@uco.es
Carlos Parés
Affiliation:
Dpto. de Análisis Matemático, Facultad de Ciencias, Universidad de Málga, Campus de Teatinos, s/n, 29071 Málaga, Spain. castor@anamat.cie.uma.es; pares@anamat.cie.uma.es
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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.

Keywords

Well-balancedfinite volume methodpath-conservativesimple Riemann solverHLLC
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 1 , January 2013 , pp. 1 - 32
Copyright
© EDP Sciences, SMAI, 2012

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