Parallel kinetic schemes for conservation laws, with large time steps

TL;DR

This paper introduces a parallel Discontinuous Galerkin method for hyperbolic conservation laws that remains stable with large time steps and enhances parallel scalability on distributed memory systems.

Contribution

It presents a novel kinetic-based parallel scheme with large time steps and a subdomain strategy for improved scalability in distributed computing environments.

Findings

Stable with large time steps without large linear system solves

Enhanced parallel scalability on distributed memory systems

Maintains explicit scheme complexity

Abstract

We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not require the assembly and resolution of large linear systems for the time iterations. The approach is based on a kinetic representation of the system of conservation laws previously investigated by the authors. In this paper, the approach is extended with a subdomain strategy that improves the parallel scaling of the method on computers with distributed memory.