A diffuse-domain-based numerical method for a chemotaxis-fluid model

Wang, Chenxi1,2; Chertock, Alina3; Cui, Shumo4; Kurganov, Alexander5; Zhang, Zhen6

2023-02-01

10.1142/S0218202523500094

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   Impact Factor & Quartile

0218-2025

1793-6314

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.

Chemotaxis Navier-Stokes equations bioconvection diffuse-domain approach finite-volume method finite-difference method

SCI

English

Corresponding

NSF["DMS-1818684","DMS-2208438"] ; NSFC["12111530004","12171226","2019B030301001"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[12071207] ; NSFC Tianyuan-Pazhou Grant[12126602] ; Natural Science Foundation of Guangdong Province[2021A1515010359]

Mathematics

Mathematics, Applied

WOS:000937169600001

WORLD SCIENTIFIC PUBL CO PTE LTD

MATHEMATICS

Web of Science

1.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
4.Southern Univ Sci & Technol, Int Ctr Math, Dept Math, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Int Ctr Math, Dept Math, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China
6.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Dept Math, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China

Wang, Chenxi,Chertock, Alina,Cui, Shumo,et al. A diffuse-domain-based numerical method for a chemotaxis-fluid model[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2023.

Wang, Chenxi,Chertock, Alina,Cui, Shumo,Kurganov, Alexander,&Zhang, Zhen.(2023).A diffuse-domain-based numerical method for a chemotaxis-fluid model.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES.

Wang, Chenxi,et al."A diffuse-domain-based numerical method for a chemotaxis-fluid model".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2023).