Operator splitting combined with positivity-preserving discontinuous Galerkin method for the chemotaxis model

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• 作者：Rongpei Zhang^a ; ^b ; ^{rongpeizhang@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jiang Zhu^b ; ^{jiang@lncc.br" class="auth_mail" title="E-mail the corresponding author} ; Abimael F.D. Loula^b ; ^{aloc@lncc.br" class="auth_mail" title="E-mail the corresponding author} ; Xijun Yu^c ; ^{yuxj@iapcm.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Chemotaxis model ; Positivity preserving ; Discontinuous Galerkin ; Krylov implicit integration factor
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：312-326
• 全文大小：1923 K

文摘

The advection–diffusion–reaction (ADR) systems are often used to describe the chemotaxis models arising in biology. In general, the stiffness from the reaction and diffusion terms often requires very restricted time step size, and the advection term depending on the concentration gradients of another component (the chemoattractant) may lead to sharp peaks in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. In this paper, we apply the operator splitting approach to solve the advection–diffusion–reaction systems. In particular, for advection term, we use the positivity-preserving DG method with strong stability preserving (SSP) high order time discretizations. For reaction–diffusion term, direct discontinuous Galerkin (DDG) method is used in spatial discretization and Krylov IIF method is applied in time discretization. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method.