Gray-Scott反应扩散模型的高效数值模拟  

Efficient Numerical Simulation of Gray-Scott Reaction-Diffusion Model

作　　者：唐思平 陈潇玥 TANG Si-ping;CHEN Xiao-yue(College of Mathematics and Physics,Xinjiang Agricultural University,Urumqi Xinjiang 830052,China)

机构地区：[1]新疆农业大学数理学院,新疆乌鲁木齐830052

出　　处：《菏泽学院学报》2024年第5期9-15,共7页Journal of Heze University

基　　金：新疆农业大学大学生创新训练计划项目(dxscx2024601)。

摘　　要：针对Gray-Scott反应扩散模型,研究了一种高效求解算法来模拟由Gray-Scott反应扩散系统所描述的动力学行为.将算法设计分为三步:首先通过维数分裂方法将高维问题分解为一系列可以并行求解的一维子问题,这有助于提升计算效率;其次,使用Crank-Nicolson格式离散每个一维子问题,并使用紧致差分格式将空间收敛阶提高到四阶;最后利用Richardson外推法提高时间收敛阶.通过数值算例验证了离散格式的有效性.An efficient solving algorithm is studied for the Gray-Scott reaction-diffusion model to simulate the dynamic behavior described by the Gray-Scott reaction-diffusion system.The algorithm design is divided into three steps.Firstly,the high-dimensional problem is decomposed into a series of one-dimensional sub-problems that can be solved in parallel through Dimension Splitting Method,which helps to improve computational efficiency.Secondly,Crack Nicolson scheme is used to discretize each one-dimensional sub-problem,and the compact difference scheme is used to increase the spatial convergence order to the fourth order.Finally,Richardson Extrapolation Method is used to improve the time convergence order,and the effectiveness of the discrete format is verified through numerical examples.

关 键 词：Gray-Scott反应扩散模型 有限差分法 维数分裂 

分 类 号：O242[理学—计算数学]