research
High-Order IMEX-RK Finite Volume Methods for Multidimensional
Hyperbolic Systems.
- Publication date
- Publisher
Abstract
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 a convective
and a non-convective part. 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. The
spatial accuracy is ensured by allowing non-oscillatory polynomial
reconstruction procedures, while the time accuracy is attained by adopting a
Runge-Kutta stepping scheme. The method can be naturally considered in the
framework of the textbf{IM}plicit-textbf{EX}plicit (IMEX) schemes and the
properties of the resulting operators are analysed using the properties of
M-matrices