Including van der Waals Forces in Diffusion-Convection Equations - Modeling, Analysis, and Numerical Simulations
Including van der Waals Forces in Diffusion-Convection Equations - Modeling, Analysis, and Numerical Simulations
复制标题
将范德华力纳入扩散-对流方程 - 建模、分析和数值模拟
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
P. Knabner
中科院分区：
文献类型：
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作者：
M. Herz;P. Knabner
本文提出了扩散-对流方程框架下的范德华力模型。该模型由一个非线性退化的扩散-对流方程组成，进一步可以认为是一个慢速循环动力学凝固的模型。在解析研究中，我们将模型转化为多孔介质方程，从而获得多孔介质方程的综合解析结果。此外，该变换还为多孔介质方程提供了新的应用。最后，通过求解多孔介质方程对该模型进行了数值模拟。我们注意到，我们在求解多孔介质方程时不需要任何进一步的正则化，而正则化通常应用于这种情况。
This paper presents a model of van der Waals forces in the framework of diffusion-convection equations. The model consists of a nonlinear and degenerated diffusion-convection equation, which furthermore can be considered as a model for slow perikinetic coagulation. For the analytical investigation, we transform the model to a porous medium equation, which provides us access to the comprehensive analytical results for porous medium equations. Additionally, this transformation reveals a new application for porous medium equations. Eventually, we present numerical simulations of the model by solving the porous medium equation. We note that we solve the porous medium equation without any further regularization, which is often applied in this context.