Xiaofeng Yang, Professor, Department of Mathematics, University of Southern Carolina, USA

Chong Chen, Associate Professor

Efficient algorithms for the anisotropic dendritic crystal models

10:00-11:00 March 28 (Tuesday), Tencent Meeting: 396-243-991, Password：311311

We consider numerical approximations of the anisotropic phase-field dendritic crystal growth model. This is a highly complex coupled nonlinear system consisting of the anisotropic Allen-Cahn equation, the heat equation, and the Navier-Stokes equation. Through the combination of the novel EIEQ approach with the novel "zero-energy-contribution" method, we develop an efficient numerical scheme with linearity, fully-decoupled structure, unconditional energy stability, and second-order time accuracy. In the process of obtaining a full decoupling structure and maintaining energy stability, the introduction of auxiliary variables and the design of their auxiliary ODEs play a vital role. The unconditional energy stability of the scheme is achieved, and the detailed implementation process is given. Through several numerical simulations of 2D and 3D dendritic crystal growth examples, the effectiveness of the developed algorithm is also verified. 

报告人简介：Dr. Xiaofeng Yang received his bachelor's and master's degree in Mathematics at the University of Science and Technology of China in 1998 and 2001, respectively. He obtained a Ph. D degree from Purdue University in 2007 and worked as a postdoctoral researcher at the University of North Carolina, Chapel Hill from 2007 to 2009. In 2009, Dr.  Yang joined the Department of Mathematics, University of Southern Carolina, and has served as Assistant Professor, Associate Professor, and Professor. Dr.  Yang's research mainly focuses on the modeling and numerical simulations of soft material, computational fluid dynamics, etc. So far, Dr. Yang has published more than 150 peer-review SCI papers, which have been cited more than 6,000 times by Google Scholar.