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. .
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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
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|
|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
To be annpounced
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.
It is desirable to have the knowledge on fundamentals of thermo-fluid dynamics and numerical analysis