DIMEX Runge–Kutta finite volume methods for multidimensional hyperbolic systems

Enrico Bertolazzi and Gianmarco Manzini

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 75, issue 5, 141-160

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.

Keywords: Finite volume; Runge–Kutta; Implicit–explicit; Partial differential equation; M-matrix (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:75:y:2007:i:5:p:141-160

DOI: 10.1016/j.matcom.2006.12.002

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