A conservative implicit multirate method for hyperbolic problems

TL;DR

This paper introduces a novel mass conservative multirate implicit method for hyperbolic equations, enabling different time steps in various spatial regions to improve efficiency while maintaining accuracy.

Contribution

It proposes a self-adjusting multirate strategy based on flux partitioning that ensures mass conservation and can be applied to various implicit discretizations.

Findings

The method achieves improved computational efficiency.

It maintains high accuracy in numerical experiments.

The approach is effective for both scalar and system hyperbolic problems.

Abstract

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from 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. It is based on flux partitioning, so that flux exchanges between a cell and its neighbors are balanced. A number of numerical experiments on both non-linear scalar problems and systems of hyperbolic equations have been carried out to test the efficiency and accuracy of the proposed approach.