Hybrid Second Order Schemes for Scalar Balance Laws

Authors:
R. Donat;A. Martinez-Gavara
Affiliations:
Departament de Matematica Aplicada, Universitat de Valencia, Burjassot, Spain 46100;Departamento de Matemática Aplicada I, E.T.S. Arquitectura, Universidad de Sevilla, Sevilla, Spain 41012
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

In this paper we explore the use of the flux-limiting technology, developed in the context of homogeneous conservation laws, in order to curb the oscillations that occur as a consequence of the plain use of data-independent second order schemes for balance laws. When trying to design high order schemes for inhomogeneous conservation laws, well balancing is one important issue that must be taken into account. The proper balance between the discretizations of the flux and the source terms is ensured by basing the design on the so-called `homogeneous form' of the balance law, postulated by Gascón and Corberán (J. Comput. Phys. 172(1):261---297, 2001).