A compact exponential method for the efficient numerical simulation of the dewetting process of viscous thin films

详细信息    查看全文

• 作者：Jorge E. Macías-Díaz ; Iliana E. Medina-Ramírez…
• 关键词：Degenerate thin ; film equation ; Compact exponential method ; Preservation of positivity ; Computationally efficient numerical technique
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：55
• 期：1
• 页码：153-174
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry;
• 出版者：Springer International Publishing
• ISSN：1572-8897
• 卷排序：55

文摘

In this work, we propose a discrete mathematical system to model the evolution of the thickness of two-dimensional viscous thin films subject to a dewetting process. The continuous model under consideration is a degenerate partial differential equation that generalizes the classical thin film equation, and considers the inclusion of a singular potential. The analytical model is discretized using an exponential method that is capable of preserving the positive character of the approximations. In addition, the explicit nature of our approach results in an economic computer implementation which produces fast simulations. We provide some illustrative examples on the dynamics of the growth of thin films in the presence/absence of a dewetting process. The qualitative results exhibit the appearance of typical patterns obtained in experimental settings. The technique was validated against Bhattacharya’s method and a standard explicit discretization of the mathematical model.