A numerical framework for singular limits of a class of reaction diffusion problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:300

Article

Moyles, Iain¹  Wetton, Brian¹ 

[1] Univ British Columbia, Inst Appl Math, Vancouver, BC V6T 1Z4, Canada

关键词: Pattern formation;    Reaction-diffusion;    Layer potentials;    Curve motion;    Mullins-Sekerka;    Curve buckling;   

DOI  :  10.1016/j.jcp.2015.07.053

来源: Elsevier

【 摘 要 】

We present a numerical framework for solving localized pattern structures of reaction-diffusion type far from the Turing regime. We exploit asymptotic structure in a set of well established pattern formation problems to analyze a singular limit model that avoids time and space adaptation typically associated to full numerical simulations of the same problems. The singular model involves the motion of a curve on which one of the chemical species is concentrated. The curve motion is non-local with an integral equation that has a logarithmic singularity. We generalize our scheme for various reaction terms and show its robustness to other models with logarithmic singularity structures. One such model is the 2D Mullins-Sekerka flow which we implement as a test case of the method. We then analyze a specific model problem, the saturated Gierer-Meinhardt problem, where we demonstrate dynamic patterns for a variety of parameters and curve geometries. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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