Effective Simulations of Interfacial Flows
Abstract
In this talk, a numerical method based on immersed boundary formulation is proposed for the simulation of two-dimensional fluid interfaces with insoluble surfactant. The governing equations are written in a mixture of Eulerian flow with Lagrangian interfacial variables and the linkage between these two set of variables is provided by the Dirac delta function. The immersed boundary force comes from the surface tension which is affected by the distribution of surfactant along the interface. By tracking the interface in a Lagrangian manner, a simplified surfactant transport equation is derived. A new symmetric discretization for the surfactant concentration equation is proposed that ensures the surfactant mass conservation numerically. By introducing an artificial tangential velocity to the Lagrangian markers, one can keep those markers uniformly distributed to have better resolution. The effect of surfactant on drop deformation in a shear flow and the moving contact line problems are investigated in detail.
About the speaker
Prof. Lai Ming-Chih received his PhD degree in Mathematics from Courant Institute of Mathematical Sciences, New York University in 1998, under the supervision of Prof. Charles S. Peskin. His PhD thesis was about introducing a new formally second-order numerical scheme with reduced numerical viscosity and validating the immersed boundary method by applying to a fluid benchmark problem which experimental data are available. His thesis won Kurt O. Friedrichs Prize for an outstanding dissertation in Mathematics at Courant Institute of NYU in 1999. After his graduation, he spent a year as a Research Associate in Physics department of Duke university. Then he returned to Taiwan and took an assistant professorship in National Chung Cheng University from August 1999 to July 2002. He moved to National Chiao Tung University in August 2002 and stays therein ever since. He is currently the chair of the Department of Applied Mathematics and the director of Institute of Mathematical Modeling and Scientific Computing in National Chiao Tung University. Prof Lai's research interests are mainly on numerical methods for PDEs and computational fluid mechanics. In particular, his work includes the improvements of immersed boundary and immersed interface methods, and their applications to fluids with interfaces. He received the Dean's Special Recognition Award in 2003 and Academic Research Award in 2005, both from National Chiao Tung University. He also received the Outstanding Research Award in 2003 from National Science Council of Taiwan.
