Asynchronous discrete event schemes for PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:342

Article

Stone, D.¹  Geiger, S.²  Lord, G. J.¹ 

[1] Heriot Watt Univ, Dept Math, Edinburgh, Midlothian, Scotland

[2] Heriot Watt Univ, Inst Petr Engn, Edinburgh, Midlothian, Scotland

关键词: Asynchronous;    Adaptive;    Discrete-event-simulation;    PDE;    Conservation laws;   

DOI  :  10.1016/j.jcp.2017.04.026

来源: Elsevier

【 摘 要 】

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both 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 reference solutions 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, and we outline a framework for analysis. (C) 2017 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free