报告题目：Energy-Stable Numerical   Schemes for Osmotic Flow through Semi-Permeable Interfaces Using Phase-Field   Method

报告人： 郭瑞晗  郑州大学

报告时间：5月23日 9:00-10:00

报告地点：管理楼1418

摘要：

We propose a thermodynamicallyconsistent phase-field model for fluid transport across semi-permeablemembranes, focusing on the effects of osmotic pressure. Unlike traditionalsharp-interface approaches, our model treats the membrane as a diffuseinterface using a phase-field formulation, allowing for natural treatmentof large deformations and topological changes. The governing equationsextend the classical Navier–Stokes–Cahn–Hilliard (NSCH) systemby incorporating an Allen–Cahn-type transmembrane flux driven by thechemical potential imbalance, resulting in a strongly coupled Navier–Stokes–Cahn–Hilliard–Allen–Cahn(NSCHAC) system. To simulate the complex interplay between solute concentration,osmotic pressure, and fluid motion, we develop energy-stable and high-ordernumerical schemes. Spatial discretization is performed using the localdiscontinuous Galerkin (LDG) method, which offers flexibility and high-orderaccuracy. For time integration, we first construct a first-order decoupledscheme with a rigorous energy stability proof, and then enhance temporalaccuracy using a semi-implicit spectral deferred correction (SDC) strategy.Numerical experiments validate the theoretical properties of the schemeand illustrate how osmotic pressure and membrane permeability influencedroplet equilibrium morphology. This framework provides a versatiletool for modeling osmotic-driven transport in biological and industrialsystems.

报告人简介：

郭瑞晗，郑州大学数学与统计学院，教授，博士生导师，郑州大学学科特聘教授。主要从事相场模型及界面问题高精度算法的研究工作，相关工作发表在SIAM   J. Sci. Comput., J. Comput. Phys., J. Sci. Comput. 等杂志。主持国家自然科学基金面上项目、青年项目、河南省自然科学优秀青年基金项目、面上项目、河南省青年人才托举工程项目。