2020 Computational Fluid Dynamics

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Academic unit or major
Graduate major in Mechanical Engineering
Xiao Feng  Aoki Takayuki 
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Course description and aims

Computational fluid dynamics is an essential and advanced tool to solve fluid mechanic problems in scientific and engineering researches. In this course, you will learn the numerical methods and stills to solve the governing equations of fluid mechanics, based on the basic knowledge of fluid mechanics and numerical analysis you have acquired in the undergraduate studies.

Student learning outcomes

The lectures will cover the fundamental numerical approaches to solve compressible and incompressible flows, as well as well other advanced topics. Students are expected to learn not only the knowledge about the numerical methods but also skills to develop computer codes through practice.


Incompressible flow, compressible flow, numerical analysis, discretization scheme, finite difference method, finite volume method, computer simulation, programming

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

We start with the governing equations of fluid mechanics, and then study discretization methods, discrete equations, typical solution methods of incompressible flows, and numerical methods for compressible flows which include TVD schemes and Riemann solvers. In addition, new developments in the field of computational fluid dynamics, such as multiphase flow simulation and high-performance computing will be also introduced.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Governing equation of fluid dynamics Derivation and phsical interpretation of mathematical equations for fluid dynamics
Class 2 Discretization methods (finite difference and finite volume methods, time-integration method), properties of discrete equations Fundamentals of discretization methods
Class 3 Numerical methods for incompressible flow (Mac,SIMPLE), Possion Solver, Multigrid Method Semi-implicit Method for incompressible flow computation
Class 4 Weakly compressible flow computation for incompressible flows, Lattice Boltzmann Method, SPH method Explicit schemes for incompressible flows
Class 5 The feature of compressible flow and the key aspects in numerical methods (Burgers equation, shock wave, conservatitve scheme) Characteristics of compressible flow, shock wave, conservative schemes, TVD schemes
Class 6 Numerical methods for compressible gas (Euler equations, Riemann solvers, high-resolution schemes) Riemann solver, implementation of TVD schemes to gas dynamics
Class 7 Numerical methods for interfacial multi-phase flows (One-fluid model, interface capturing methods, surface tension) One-fluid model, interface capturing methods, surface tension

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


To be annpounced

Reference books, course materials, etc.

1. 肖鋒,長崎孝夫:「数値流体解析の基礎 - Visual C++とgnuplotによる圧縮性・非圧縮性流体解析」,コロナ社,2020年(in Japanese)
2. Anderson, J.D., Computational Fluid Dynamics - The Basics with Applications; McGraw-Hill, Inc. 1995
3. Hirsch C., Volume 1&2, Numerical Computational of Internal and External Flows; John Wiley & Sons, 2001
4. Ferziger, J.H. and Peric, M., Computational Methods for Fluid Dynamics; Springer, 1999

Assessment criteria and methods

Learning achievement is evaluated by reports and excercises, and programing practice may be required in some cases.

Related courses

  • MEC.F201 : Fundamentals of Fluid Mechanics
  • MEC.F211 : Practical Fluid Mechanics
  • MEC.F331 : Advanced Fluid Mechanics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is desirable to have the knowledge on fundamentals of thermo-fluid dynamics and numerical analysis

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