An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Abstract

In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.

Type
Publication
Journal of Computational Physics (405)
Huaxiong Huang
Huaxiong Huang
Professor

Huaxiong Huang is Professor of Mathematics at the York University. He is VP (Academic) and Executive Director of Research Center of Mathematics (Zhuhai, China). He has served as Deputy Director of the Fields Institute and Director of the Fields Centre for Quantitative Analysis and Modelling. His wide array of publications in applied mathematics focus on fluid mechanics and scientific computing, finance, biology, physiology, energy and medicine.

Zilong Song
Zilong Song
Assistant Professor

Dr. Song received his Ph.D. in applied mathematics from City University of Hong Kong. Dr. Song was a postdoctoral fellow at York University and [Fields Institute}(https://www.fields.utoronto.ca). Dr. Song worked at UC Riverside as a visiting assistant professor, before joining Utah State University in 2021. Dr. Song works in interdisciplinary areas of applied mathematics, including ion transport systems, disease modeling, continuum mechanics etc. He has also been working on asymptotic analysis of systems with small parameters or special structures. Dr. Song is interested in modeling, analysis and computation of various biological systems.

Shixin Xu
Shixin Xu
Assistant Professor

Shixin Xu is an Assistant Professor of Mathematics at Duke Kunshan University. His research interests are machine learning and data-driven models for diseases, multiscale modeling of complex fluids, homogenization theory, and numerical analysis. Xu has a B.Sc. in mathematics (honors) from Ocean University of China and a Ph.D. in mathematics from the University of Science and Technology China. From 2013 to 2017, he held postdoctoral positions at the National University of Singapore, the University of Notre Dame, the University of California, Riverside, and the Fields Institute for Research in Mathematical Sciences, Canada.