Asynchronous Discrete Event Schemes for PDEs

TL;DR

This paper introduces a novel asynchronous discrete-event simulation method for PDEs, enabling self-adaptive, local-in-time solutions for complex advection-diffusion-reaction systems, with demonstrated first-order convergence in realistic 3D applications.

Contribution

It presents a new asynchronous scheme for PDEs that is self-adaptive and local, validated on realistic porous media flow problems, and compares favorably to exponential integrator benchmarks.

Findings

First-order convergence observed as control parameter decreases

Method performs well on large 3D advection-diffusion problems

Accurate error estimation achieved through comparison with exponential integrators

Abstract

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The timescales of these events are linked to the flux on the the face, and the schemes are self-adaptive, local in time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate results where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased.