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

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • E. Bertolazzi

    (Dipartimento di Ingegneria Meccanica e Strutturale)

  • G. Manzini

    (IMATI-CNR)

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.

Suggested Citation

  • E. Bertolazzi & G. Manzini, 2003. "High-order IMEX-RK finite volume methods for multidimensional hyperbolic systems," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 35-44, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_3
    DOI: 10.1007/978-88-470-2089-4_3
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