## Course Title : Computational Fluid Dynamics

Code 10F011 Master and Doctor Course 2nd term Mon 4th C1-172 2 No Restriction Lecture English Satoru Ushijima, Hitoshi Gotoh, Abbas Khayyer

### Course Description

Computational Fluid Dynamics (CFD) is largely developed according to the progress of computer technology in recent years. It is the powerful and effective technique to predict the various fluid phenomena, which show the complicated behaviors due to the non-linearity and other conditions. This course provides the dynamics of fluids and eddies as well as the discretization and numerical techniques, such as finite difference, finite volume and particle methods.

The grading will be based on homework assignments.

### Course Goals

Course goal is to understand the basic theory and numerical techniques for CFD.

### Course Topics

Theme Class number of times Description
Introduction 1 Introduction of recent examples of CFD
computational method for incompressible fluids 7 The course introduces the MAC algorithm, which is generally used for incompressible Newtonian fluids on the basis of finite difference and finite volume methods (FDM and FVM). The outline of numerical methods is also discussed for parabolic, hyperbolic or elliptic partial differential equations, in terms of the numerical stability and accuracy. Homework will be assigned each week.
Particle method - basic theory and improvements 7 To simulate violent flow with gas-liquid interface which is characterized by fragmentation and coalescence of fluid, particle method shows excellent performance. Firstly, basics of the particle method, namely discretization and algorithm, which is common to SPH(Smoothed Particle Hydrodynamics) and MPS(Moving Particle Semi-implicit) methods, are explained. Particle method is superior in robustness for tracking complicated interface behavior, while it suffers from existence of unphysical fluctuation of pressure. By revisiting the calculation principle of particle method, various improvements have been proposed in recent years. In this lecture, the state-of-the-art of accurate particle method is also described.

### Textbook

No textbook assigned to the course

### Textbook(supplemental)

Recommended books and papers will be introduced in the course.

### Prerequisite(s)

Basic knowledge of fluid dynamics, continuum mechanics and computational technique