Clarelli F, Di Russo C, Natalini R, Ribot M
Istituto per le Applicazioni del Calcolo "M.Picone", sez. Firenze, Consiglio Nazionale delle Ricerche, Polo Scientifico-Edificio F, CNR, 50019 Sesto Fiorentino, FI, Italy.
J Math Biol. 2013 Jun;66(7):1387-408. doi: 10.1007/s00285-012-0538-5. Epub 2012 May 5.
A system of nonlinear hyperbolic partial differential equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simulations will be presented in one and more space dimensions in the particular case of cyanobacteria biofilms. Besides, the numerical scheme we present is able to deal in a natural and effective way with regions where one of the phases is vanishing.
利用混合理论推导了一个非线性双曲型偏微分方程组，用于对生物膜的形成进行建模。与大多数现有模型不同的是，我们的方程具有有限的传播速度，无需使用人工自由边界条件。将详细描述适用的数值格式，并在蓝藻生物膜的特定情况下，给出一维和多维空间的若干模拟结果。此外，我们提出的数值格式能够自然有效地处理其中一个相消失的区域。
