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 lecture on the numerical schemes for compressible flow, e.g., the TVD scheme. The cource advances to to lecture on parallel computing and recent development in computational fluid dynamics.
|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 (Poisson equation for pressure ans MAC method)||MAC(Marker and cell) method|
|Class 6||Governing equation for compressible flows and its characteristic feature||Characteristic features of compressible flow|
|Class 7||Numerical methods for compressible flows (Riemann solver and construction of high-resolution ,method)||Riemann solver|
|Class 8||Large-scale parallel computation, Lattice Bolzman method, Review of free surface multi-phase flow)||Advanced method in numerical analysis|
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