Speaker: 徐立伟教授，电子科技大学

Inviter: 中国科学院数学院学术报告会组委

Title: Modelling and simulation of flow dynamics in electromagnetic fields

Language: Chinese

Time & Venue: 2025.06.20 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: The talk is devoted to presenting the dynamic behavior of flows in electromagnetic fields. Based on different interaction mechanisms with electromagnetic fields, we mainly investigate three classes of hydrodynamics, the magnetohydrodynamics (MHD) , ferrohydrodynamics (FHD) and optical hydrodyamics . For MHD systems, which describes electrically conductive fuilds under the influence of Lorentz forces, we consider the two phase flow dynamics governed by the Cahn-Hilliard-MHD equation and the Abels--Garcke--Grün--MHD equation. An unconditionally energy-stable and convergent convex splitting FEM scheme will be proposed and analyzed. Then, we consider the FHD system, which characterizes the magntized fluids subjected to Kelvin force in the presence of external magnetic fields. We propose a novel sharp interface model for the two phase FHD system, and use the mesh moving methods to solve the proposed model. The classic benchmarks of the FHD system, “Rosensweig instability” phenomena, are simulated by imposing the uniform and nonuniform magnetic fields both in 2D and 3D. Finally, we study the semi-classical Hamiltonian of the electron system and develop a generalized hydrodynamic Drude (GHD) model that includes the electron spill-out effect and tunnelling for small metallic nanostructures. The model incorporates a non-uniform electron density distribution, which is derived self-consistently from the energy functional of the electron system. We design a high-order discontinuous Galerkin method for which essential numerical analysis on the stability and accuracy is carried out, and present numerical results of some important optical phenomenon for the validation of the model and the scheme.