The content discusses the development of efficient numerical schemes for a class of fast reaction-diffusion systems, where the reaction terms are much larger than the diffusion terms. The key highlights are:
The authors consider a special type of fast reaction-diffusion system with two reactants and one substrate, where the dynamics of the reactants are governed by both diffusion and fast reactions, while the substrate's evolution is only determined by fast reactions.
The authors propose a semi-implicit scheme that is first-order accurate in time. This scheme satisfies the non-negativity, bound preserving properties, and has L2 stability. It can accurately capture the interface propagation even when the reaction becomes extremely fast.
The authors also construct a semi-implicit Runge-Kutta scheme that is second-order accurate in time, following the methodology presented in previous work.
Numerical tests are carried out to demonstrate the properties of the proposed schemes, such as accuracy, positivity, bound preserving, and the ability to capture sharp interfaces. Simulations of the dynamics of substances in chemical reactions and the heat transfer process (e.g., melting or solidification) are also presented.
The authors show that the limit behavior of the fast reaction-diffusion system is described by the Stefan problem as the reaction rate becomes extremely large. They provide error estimates of the numerical schemes with respect to the reactivity coefficients.
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arxiv.org
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by Yu Zhao,Zhen... ב- arxiv.org 04-30-2024
https://arxiv.org/pdf/2404.18463.pdfשאלות מעמיקות