A CONSERVATIVE IMPLICIT MULTIRATE METHOD FOR HYPERBOLIC PROBLEMS

Time: 12:45 - 13:30, April 18
Room: 5.09

Abstract

Abstract: Conservation laws model a large variety of phenomena in geophysical flows, typical examples are shallow water flow, multiphase groundwater flow, advection and dispersion of contaminants, etc. The time discretization of hyperbolic problems is often subject to restriction of the time step. Explicit time integration schemes are only stable if the time step amplitude full fills the CFL condition. It is also possible to use an implicit, method but all high order implicit scheme are not unconditionally monotone, a different condition for the size of time step is required to ensure monotonicity. To overcome this problem, we focus on a self-adjusting multirate strategy based on an implicit method that could benefit from different time steps in different areas of the spatial domain. We propose a novel formulation of a mass conservative multirate approach, that can be generalized to various implicit time discretization methods. It is based on a flux partitioning, so that flux exchanges between a cell and its neighbours are balanced. A number of numerical experiments on both non-linear scalar problems and systems of equations have been carried out to test the efficiency and accuracy of the proposed approach.