报告题目： Mathematical modeling and numerical simulation of surfactant systems with incompressible N-S equations on surfaces
报告人：冯新龙教授
工作单位：新疆大学
报告时间：2021-11-27(周六) 15：00-17:00
腾讯会议：496-138-446
摘要：
In this work, the mathematical modeling and numerical approximation for the fluid-surfactant phase field model coupled with Navier-Stokes equations on surfaces are considered. Taking account of the effect of the curvature and fluid flows, we first propose the model on surfaces. Then, by introducing two power-type scalar auxiliary variables in the phase field equations for the potential energy terms and an exponential-type one in the momentum equation with respect to the inertial term, we transform the proposed model to an equivalent form. Furthermore, via utilizing the pressure correction method and implicit-explicit techniques in a proper sequence to eliminate the influence of the skew-symmetric loss in the standard surface FEM, and applying stabilized methods for the convective and diffusion terms in the phase field and momentum equations according to the feature of the velocity field on surfaces respectively, we construct a linearized and decoupled fully discrete scheme, in which only some linear equations need to be solved at each time step. Unconditional energy stability of the fully discrete scheme is also proved. Finally, numerical examples are shown to verify the rationality of the model and the efficiency of the proposed schemes.
报告人简介：
冯新龙，新疆大学数学与系统科学学院，博士，教授，博士生导师。研究领域：科学计算、计算流体力学、不确定性量化、人工智能与机器学习等。1994-1998 新疆大学基础数学（软件工程）专业本科毕业；1998-2001新疆大学计算数学专业硕士毕业；2003-2007西安交通大学数学专业博士毕业。曾在韩国首尔国立大学、香港浸会大学、巴西巴拉那联邦大学、加拿大阿尔伯塔大学从事博士后研究和访问学习。拥有中国准精算师资格，曾担任中国核学会计算物理学会理事、中国计算数学学会理事、中国数学会理事等。曾荣获自治区科学技术进步奖【自然科学奖】一等奖1项，二等奖1项；自治区高等教育教学成果二等奖2项。研究成果相继发表在SINUM，SISC, MCOM, CMAME, JCP, JSC,IJHMT等国际权威期刊。
