High-order IMEX-RK finite volume methods for multidimensional hyperbolic systems

E. Bertolazzi and G. Manzini
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E. Bertolazzi: Dipartimento di Ingegneria Meccanica e Strutturale
G. Manzini: IMATI-CNR

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 35-44 from Springer

Abstract: Summary In this paper we present a high-order accurate cell-centered finite volume method for the semi-implicit discretization of multidimensional hyperbolic systems in conservative form on unstructured grids. This method is based on a special splitting of the physical flux function into convective and non-convective parts. The convective contribution to the global flux is treated implicitly by mimicking the upwinding of a scalar linear flux function while the rest of the flux is discretized in an explicit way. Spatial accuracy is ensured by allowing nonoscillatory polynomial reconstruction procedures, while time accuracy is attained by adopting a Runge-Kutta stepping scheme. The method can be considered naturally in the framework of the implicit-explicit (IMEX) schemes and the properties of the resulting operators are analysed using the properties of M-matrices.

Keywords: Flux Function; Numerical Flux; Flux Form; Convective Contribution; Polynomial Reconstruction (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2089-4_3

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DOI: 10.1007/978-88-470-2089-4_3

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