2018 Computational Thermo-Fluid Dynamics

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Academic unit or major
Graduate major in Mechanical Engineering
Horiuti Kiyosi  Xiao Feng 
Class Format
Media-enhanced courses
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Course description and aims

This course focuses on the numerical analysis of thermo-fluid dynamics which constitutes one of the fundamentals in mechanical engineering.. By combining lectures and exercises, the course enables students to acquire the ability to apply the achieved knowledge to solve numerically the application problems in thermo-fluid dynamics. .

Student learning outcomes

We aim to teach fundamentals and applications of the numerical analysis to solve the problems in incompressible and compressible thermo-fluid dynamics. Students will learn about the finite difference and finite volume methods.


Incompressible flow, compressible flow, numerical analysis, discretization scheme

Competencies that will be developed

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

Class flow

After showing fundamentals of the governing equations, classes are devoted to Poisson-equation solver, treatment of the convective term (upwind method), time-integration methods. and then standard numerical schemes for incompressible flow. We proceed to lectures on the numerical schemes for compressible flow, e.g., the TVD scheme. Advanced topics, such as the numerical simulations of interfacial multiphase flows, will be introduced as well.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Governing equation of Thermo-Fluid Dynamics, Partial differential equation, fundamentals of diffusion equation and wave equation Fundamentals of partial differential equation
Class 2 Discretization methods for partial diferential equation (finite difference and finite volume methods, time-integration method) Fundamentals of discretization methods
Class 3 Stability and truncation error analysis of the discretization methods Fundamentals of stability and truncation error analysis
Class 4 Governing equation for incompressible flows and its characteristic features Characteristic features of incompressible flow
Class 5 Numerical methods for incompressible flows (MAC method and SIMPLE method) MAC method and SIMPLE method
Class 6 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 7 Numerical methods for compressible gas (Euler equations, Riemann solvers, high-resolution schemes) Riemann solver, implementation of TVD schemes
Class 8 Numerical methods for interfacial multi-phase flows (One-fluid model, interface capturing methods, surface tension) One-fluid model, interface capturing methods, surface tension


To be annpounced

Reference books, course materials, etc.

To be annpounced

Assessment criteria and methods

Students' knowledge of basic topics of numerical methods in thermal-fluid dynamics, and their ability to apply them to engineering problems will be assessed. .Learning achievement is evaluated by reports and excercises.

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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