Numerical investigation of chemotaxic phenomenon in incompressible viscous fluid flow

Abstract

This study aims to get some details of the chemotaxic phenomena in a domain containing an incompressible viscous fluid by the proposed numerical method. We are also aimed to numerically revisit the classical blow-up phenomenon regarding the initially prescribed cell density in an infinitely larger domain. To get a computationally more accurate scheme for solving the Keller-Segel (KS) [1] equations with/without coupling with the nonlinear hydrodynamic equations, a combined compact difference scheme of fifth-order spatial accuracy is developed in a three-point grid stencil. Three different sets of Keller-Segel equations, which are all amenable to exact solutions with/without coupling with the incompressible Navier–Stokes (NS) equations, are solved to numerically verify the proposed combined compact difference scheme and the incompressible flow solver. How the cell density and chemical concentration are affected by flow convection and diffusion effects will be investigated by solving the coupled KS–NS differential equations.