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应用数学进展  >> Vol. 6 No. 3 (May 2017)

一种用于反应扩散方程的格子Runge-Kutta-Boltzmann模型
A Lattice Runge-Kutta-Boltzmann Model for the Reaction Diffusion Equation

DOI: 10.12677/AAM.2017.63047, PDF, HTML, XML, 下载: 937  浏览: 1,181  国家自然科学基金支持

作者: 闫铂, 王建朝：吉林建筑大学土木工程学院，吉林 长春；闫广武：吉林大学数学学院，吉林 长春

关键词: 格子Boltzmann模型；Runge-Kutta公式；反应扩散方程；Latctice Boltzmann Model； Runge-Kutta Scheme； Reaction Diffusion Equation

摘要: 本文构建了一个求解反应扩散方程的格子Runge-Kutta-Boltzmann模型。通过使用经典的Runge-Kutta公式，得到了四阶截断误差。通过Chapmann-Enskog展开和多尺度展开技术，获得了不同时间尺度的系列偏微分方程和修正的反应扩散方程。数值结果表明，本文的模型可以用来求解反应扩散方程。
Abstract: A lattice Runge-Kutta-Boltzmann model for the reaction diffusion equations is constructed in this paper. By using the classical Runge-Kutta formula, we obtain four-order accuracy of truncation error. The Chapman-Enskog expansion and multi-scale technique are employed in order to obtain a series of equations in different time scales and modify partial differential equations of the reaction diffusion equations. Numerical tests show that the scheme can be used to simulate the reaction diffusion equations.

文章引用: 闫铂, 王建朝, 闫广武. 一种用于反应扩散方程的格子Runge-Kutta-Boltzmann模型[J]. 应用数学进展, 2017, 6(3): 408-416. https://doi.org/10.12677/AAM.2017.63047

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