讲座题目：A Semi-Lagrangian Approach for Incompressible Flows

报告人：Prof. Tameo Nakanishi

时 间：9月23日（周四）下午3:30
地 点：力学楼434会议室
主持人：王健平(教授)

报告内容摘要：
      Accurate and efficient simulation of fluid flows requires adequate choice of the Lagrangian or the Euler framework. The conventional Euler framework based flow simulation method is subject to restriction on the CFL number. Here, we present a semi-Lagrangian (SL) approach for incompressible flows. This approach deals with the advection phase by an explicit SL model of third order accuracy and the viscous term by the modified Crank-Nicholson method. The scheme is free from the CFL condition and allows a large time step. The scheme is proven very effective for advection dominated unsteady flow of relatively large time scale. This approach has been incorporated into an incompressible flow solver of using curvilinear overset grid system, which can simulate flow problems with complex geometry and multiple bodies in both 2D and 3D.
     An interactive two-dimensional flow simulation system for educational use has been developed based upon the above approach. The system can instantly generate arbitrary body shape and computational meshes around the bodies, perform real-time simulation, and display simulation results. The system is very flexible and easy-to-use, requiring no pre-knowledge of fluid mechanics and numerical simulation. Demonstration of the system will be made at the seminar.
     A new method of employing the advection equation of the initial coordinates along with the SL method was proposed to accurately track multiple types of fluids in the stationary grid system. The method is called Transport Coordinate (TC) Method. The method has much less numerical diffusion as compared with the conventional VOF method, and exhibits improved mass conservation performance. The method is applicable to the advection function of arbitrary distribution, for example, problems with more than two types of fluids. Examples of two-phase flow simulations will be given.

报告人简介：
      Dr. Tameo Nakanishi earned his PH.D. in the Department of Aeronautical Engineering at Nagoya University in 1991. He is currently an associate professor in Mechanical Systems Engineering Branch, Graduate School of Engineering, Yamagata University, Japan. His research areas are mainly about the development and applications of numerical method to solve incompressible flows.