Title： Normal Mode Analysis of 3D Incompressible Viscous Fluid Flow Models

Speaker： Professor Guoping Zhang  （Morgan State University, USA）

Time： 2019年7月8日        上午  10:00-11:00

Room： 东区第五教学楼  5205室

Abstract： Many types of flow motions can be described by using various forms of incompressible viscous flow models. In particular, the incompressible Navier-Stokes equations have been widely used to model many important applications such as ocean currents, water flow in a pipe, water pollution, and blood flow in vessels. We study the normal mode solutions of 3D incompressible viscous fluid flow models. The obtained theoretical results are then applied to analyze several time-stepping schemes for the numerical solutions. In the normal mode analysis, we first linearize the nonlinear model (if the original model is nonlinear), then we find all possible eigenfunctions (so called normal modes) of the eigenvalue problem associated with the linearized model. In general the solution of the linearized model is a superposition of the normal modes. Therefore we only need to test the stability of each normal mode solution in order to test it for the arbitrary solution of the problem.This is a joint work with Mingchao Cai.