New resolution strategy for multi-scale reaction waves using time operator splitting, space adaptive multiresolution and dedicated high order implicit/explicit time integrators

Description

In this paper, we tackle the numerical simulation of reaction-diffusion equations modeling multiscale reaction waves. This type of problems induces peculiar diffculties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts which are spatially very localized. In a series of previous studies, the numerical analysis of operator splitting techniques has been conducted and such an approach has shown a great potential in the framework of reaction-diffusion and convection-diffusion-reaction systems. However, even if a firm theoretical background is available, an optimal strategy for high performance numerical simulation is still needed. In this paper, we introduce a new strategy for reaction-diffusion systems based on time operator splitting in the context of very localized and very stiff reaction fronts. It provides an optimal combination of adaptive spatial multiresolution, implicit resolution of reaction and explicit resolution of diffusion. The optimality is reached in terms of the choice of the operator splitting time step which, in the framework of self-similar reaction waves, allows a very good combination of the various dedicated solvers used in the proposed strategy. The computational effciency is then evaluated through the numerical simulation of configurations which were so far out of reach of standard methods in the field of nonlinear chemical dynamics for spiral waves and scroll waves as an illustration.

Abstract

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