A robust explicit asynchronous time integration method for hyperbolic conservation laws

Abstract
Hyperbolic conservation laws are of great practical importance as they model diverse multiscale phenomena (highly turbulent flows, combustion, etc.). To solve these equations, explicit time integration methods are used, for which the Courant–Friedrichs–Lewy (CFL) condition has to be satisfied everywhere in the computational domain. Therefore, the global time step will be dictated by the cells that require the smallest time step, resulting in an unnecessarily expensive computational approach. To overcome this difficulty, a conservative asynchronous method for explicit time integration schemes is developed and implemented for flux-based spatial schemes. The concept of the developed method is using dynamically variable time steps for classes of cells, while ensuring the time coherence of the time integration and flux conservation. In this paper, we present the classification of computational cells in classes based on their local stability criterion. Two versions of the (asynchronous) synchronization sequence are proposed, which are designed regardless of equation model and spatial scheme. In the context of hyperbolic conservation laws, we numerically investigate the conservation, accuracy and stability properties of the proposed method for one-dimensional linear convection and Euler equations. We show that the proposed asynchronous approach can be more accurate than its synchronous counterpart through the limitation of the diffusion errors by locally increasing the CFL number and thus, the local time step.

Citation
Messahel, R., Boutsikakis, A., Grondin, G., Gressier, J., Parsani, M., & Boukharfane, R. (2021). A robust explicit asynchronous time integration method for hyperbolic conservation laws. AIAA Scitech 2021 Forum. doi:10.2514/6.2021-0054

Publisher
American Institute of Aeronautics and Astronautics (AIAA)

Conference/Event Name
AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2021

DOI
10.2514/6.2021-0054

Additional Links
https://arc.aiaa.org/doi/10.2514/6.2021-0054

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