论文标题
抛物线变异不平等系统模拟生物膜生长的数值分析
Numerical Analysis of a Parabolic Variational Inequality System Modeling Biofilm Growth at the Porescale
论文作者
论文摘要
在本文中，我们考虑了两个耦合非线性扩散 - 反应部分微分方程（PDE）的系统，该系统对生物膜的生长和养分消耗进行了建模。在感兴趣的规模上，生物膜密度受到点的约束，因此生物膜PDE被构架为抛物线变异不平等。我们对耦合的非线性系统进行有限元（Fe）近似的严格误差估计值，并通过实验确认数值以预测速率收敛。我们还显示了模拟，其中我们在域中跟踪类似于孔隙尺度几何形状的域中的自由边界，并在其中测试不同的建模假设。
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject to a pointwise constraint, thus the biofilm PDE is framed as a parabolic variational inequality. We derive rigorous error estimates for a finite element (FE) approximation to the coupled nonlinear system and confirm experimentally that the numerical approximation converges at the predicted rate. We also show simulations in which we track the free boundary in the domains which resemble the pore scale geometry and in which we test the different modeling assumptions.
