A diffuse-domain-based numerical method for a chemotaxis-fluid model
A diffuse-domain-based numerical method for a chemotaxis-fluid model
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DOI：
10.1142/s0218202523500094
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发表时间：
2023-02-23
影响因子：
3.5
通讯作者：
Zhang, Zhen
中科院分区：
文献类型：
--
作者：
Wang, Chenxi;Chertock, Alina;Zhang, Zhen
在本文中，我们考虑一个耦合趋化性流体系统，模型自组织集体行为的趋氧细菌在一个固着滴。该模型描述了流体环境中的生物趋化现象，并将耗氧趋氧细菌的对流趋化系统与重力作用下的不可压Navier-Stokes方程耦合起来，该方程与细胞密度相对于水密度的相对盈余成正比，发展了一种新的保正性和高分辨率的趋化-流体系统方法.我们的方法是基于扩散域的方法，我们用它来获得一个新的趋化性流体扩散域（cf-DD）模型模拟生物对流在复杂的几何形状。将液滴区域嵌入到一个较大的矩形区域中，用一个有限厚度的扩散界面代替原来的边界。原始趋化性流体系统重新制定的更大的域上的附加源项，近似的物理界面上的边界条件。我们发现，cf-DD模型收敛到趋化性流体模型渐近扩散界面的宽度收缩为零。我们数值求解所得到的cf-DD系统的二阶混合有限体积有限差分法，并展示了所提出的方法的性能上的一些数值实验，展示了几个有趣的趋化现象，在不同形状的固着液滴，其中细菌的图案取决于液滴的几何形状。
In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biological chemotaxis phenomenon in the fluid environment and couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier-Stokes equations subject to a gravitational force, which is proportional to the relative surplus of the cell density compared to the water density.We develop a new positivity preserving and high-resolution method for the studied chemotaxis-fluid system. Our method is based on the diffuse-domain approach, which we use to derive a new chemotaxis-fluid diffuse-domain (cf-DD) model for simulating bioconvection in complex geometries. The drop domain is imbedded into a larger rectangular domain, and the original boundary is replaced by a diffuse interface with finite thickness. The original chemotaxis-fluid system is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the physical interface. We show that the cf-DD model converges to the chemotaxis-fluid model asymptotically as the width of the diffuse interface shrinks to zero. We numerically solve the resulting cf-DD system by a second-order hybrid finite-volume finite-difference method and demonstrate the performance of the proposed approach on a number of numerical experiments that showcase several interesting chemotactic phenomena in sessile drops of different shapes, where the bacterial patterns depend on the droplet geometries.