Numerical simulation of chemotaxis models on stationary surfaces
Numerical simulation of chemotaxis models on stationary surfaces
复制标题
DOI：
10.3934/dcdsb.2013.18.2689
复制
发表时间：
2013-10
影响因子：
1.2
通讯作者：
A. Sokolov;R. Strehl;S. Turek
中科院分区：
文献类型：
--
作者：
A. Sokolov;R. Strehl;S. Turek
在本文中，我们提出了一种用于一类趋化性模型的隐式有限元方法，其中修改了新的线性化通量校正传输（FCT）算法，以保持表面活细胞的密度非负。采用水平集技术来隐式描述表面以及相应的偏微分方程组的数值处理。所提出的方案能够为一大类趋化性驱动模型提供稳健且准确的解决方案。所提出方案的数值行为在球体和椭球体上的爆炸模型以及球体上大肠杆菌的图案形成动力学模型上进行了测试。
In this paper we present an implicit finite element method for a class of chemotaxis models, where a new linearized flux-corrected transport (FCT) algorithm is modified in such a way as to keep the density of on-surface living cells nonnegative. Level set techniques are adopted for an implicit description of the surface and for the numerical treatment of the corresponding system of partial differential equations. The presented scheme is able to deliver a robust and accurate solution for a large class of chemotaxis-driven models. The numerical behavior of the proposed scheme is tested on the blow-up model on a sphere and an ellipsoid and on the pattern-forming dynamics model of Escherichia coli on a sphere.