A conservative implicit multirate method for hyperbolic problems

Abstract

This work focuses on the improvement of a self-adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations that allows to employ different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach that can be generalized to various implicit time discretization methods. Mass conservation is achieved by flux partitioning, so that mass exchanges between a cell and its neighbors are exactly balanced. A number of numerical experiments on both nonlinear scalar problems and systems of hyperbolic equations have been carried out to test the efficiency and accuracy of the proposed approach.