Bound/Positivity Preserving Sav Schemes for the Patlak-Keller-Segel-Navier-Stokes System

作     者：Huang, Xueling Shen, Jie 

作者机构：School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian Xiamen361005 China Department of Mathematics Purdue University West LafayetteIN47907 United States 

出 版 物：《SSRN》 

年 卷 期：2022年

核心收录：

主　　题：Energy dissipation 

摘      要：The Patlak-Keller-Segel-Navier-Stokes system describes the biological chemotaxis phenomenon in the fluid environment. It is a coupled nonlinear system with unknowns being the cell density, the concentration of chemoattractants, the fluid velocity and the pressure, and it satisfies an energy dissipation law, preserves the bound/positivity and mass of the cell density. We develop in this paper a class of scalar auxiliary variable (SAV) schemes with relaxation which preserve these properties unconditionally at the discrete level, and only require solving decoupled linear systems with constant coefficients at each time step. We present ample numerical results to validate these schemes, and investigate the blow-up phenomenon. In particular, it is found that the fluid flow could delay the blow-up time when compared with the PatlakKeller-Segel system without flow, but weather it may surpress the blow-up requires further investigation. © 2022, The Authors. All rights reserved.