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DIMEX Runge–Kutta finite volume methods for multidimensional hyperbolic systems

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  • Bertolazzi, Enrico
  • Manzini, Gianmarco

Abstract

We propose a class of finite volume methods for the discretization of time-dependent multidimensional hyperbolic systems in divergence form on unstructured grids. We discretize the divergence of the flux function by a cell-centered finite volume method whose spatial accuracy is provided by including into the scheme non-oscillatory piecewise polynomial reconstructions. We assume that the numerical flux function can be decomposed in a convective term and a non-convective term. The convective term, which may be source of numerical stiffness in high-speed flow regions, is treated implicitly, while the non-convective term is always discretized explicitly. To this purpose, we use the diagonally implicit–explicit Runge–Kutta (DIMEX-RK) time-marching formulation. We analyze the structural properties of the matrix operators that result from coupling finite volumes and DIMEX-RK time-stepping schemes by using M-matrix theory. Finally, we show the behavior of these methods by some numerical examples.

Suggested Citation

  • Bertolazzi, Enrico & Manzini, Gianmarco, 2007. "DIMEX Runge–Kutta finite volume methods for multidimensional hyperbolic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(5), pages 141-160.
    • Handle: RePEc:eee:matcom:v:75:y:2007:i:5:p:141-160
    DOI: 10.1016/j.matcom.2006.12.002
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    Cited by:

    1. Manzini, Gianmarco, 2009. "A second-order TVD implicit–explicit finite volume method for time-dependent convection-reaction equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2403-2428.

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