Continuous finite element schemes for a phase field model in two-layer fluid Bénard-Marangoni convection computations

In this paper, we study a phase field model for a two-layer fluid where the temperature dependence of both the density (buoyancy forces) and the surface tension (Marangoni effects) is considered. The phase model consisting of a modified N-S equation, a Cahn-Hilliard phase field equation and an energy transport equation is derived through an energetic variational procedure. An appropriate variational form and a continuous finite element method are adopted to maintain any possible underlying energy law to its greatest extent. A few examples for Benard-Marangoni convection in an Acetonitrile and an n-Hexane two-layer fluid system heated from above will be computed to justify our phase field model and further show the good performance of our methods. In addition, an interesting experiment will be performed to show the competition between the Marangoni effects and the buoyancy forces. Suggested Reviewers: Xiaofeng (Michael) Yang PhD Assistant Professor, Mathematics, University of South Carolina, USA [email protected] expert in phase field model computation. Zhilin Li PhD Professor, Mathematics, North Carolina State University, Raleigh, NC [email protected] expert in fluid interface problems James J. Feng PhD Professor, Chemical and Biological Engineering and Mathematics, University of British Columbia, Canada [email protected]; [email protected] expert in complex fluids and interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Continuous Finite Element Schemes for a Phase Field Model in Two-Layer Fluid Bénard-Marangoni Convection Computations Z. Guo, P. Lin ∗1, and Y. Fan 1Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom. 2Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, China 3College of Marine Life Science, Ocean University of China, Qingdao, 266071, China