COMPUTATIONAL FLUID DYNAMICS
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- Versione italiana
- Academic year
- 2021/2022
- Teacher
- WALTER BOSCHERI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/08
Training objectives
- The course aims at furnishing knowledge and skills for the numerical solution of problems in fluid dynamics.
The principal goals of the course are as follows:
- knowledge of the equations and the numerical solution of hyperbolic differential equations (linear and nonlinear case);
- numerical algorithms based on finite volume and finite difference discretization. Multidimensional extension and implementation of numerical schemes.
The main competences that need to be learnt are as follows:
- identification of the type of governing equations;
- choice of the better approach for the numerical solution of a given set of equations;
- capability of implementation of numerical schemes in multiple space dimensions for a range of physically meaningful problems. Prerequisites
- The course reqires an excellent knowledge of differential calculus. Good programming skills in Matlab are also recommended.
Course programme
- 1. Introduction to conservation laws. Scalar linear and nonlinear case, nonlinear hyperbolic systems of balance laws. (9 hours)
2. Shock waves, Rankine-Hugoniot conditions and Riemann problem. Exact and approximate Riemann solvers. (9 hours)
3. Multidimensional finite volume methods on unstructured meshes. Second order TVD methods in space and time. (10 hours)
4. Applications to Euler and shallow water equations with solid transport. (10 hours)
5. Numerical methods for incompressible flows: semi-implicit schemes and SIMPLE method. (10 hours) Didactic methods
- The course is composed of a first part of theoretical lessons (18 hours) and a second part of practical lessons (30 hours).
Learning assessment procedures
- The exam is composed of two parts: a programming project and an oral interview which equally contributes to the final mark (arithmetic average of the marks for each of the two parts).
Reference texts
- R.J. LeVeque. Numerical methods for Conservation Laws. Lectures in Mathematics. ETH Zürich (1992).
