Image
Numerical methods for fluid dynamics
Numerical simulation is playing an expanding role in the study of fluid dynamics and often complements experiments and theory. In this course, we will introduce and analyse the various methods available to solve the partial differential equations relevant to fluid dynamics. We will study their application to a wide variety of problems and highlight the effects of discretisation strategies. The objective of the course is to gain a practical knowledge, but also a general view of the existing methods and the ability to decide on the best suited choice for a given problem.
Emphasis will be placed on algorithms and their convergence properties as well as applications to a wide variety of fluid dynamics problems.
Syllabus
Some or all of the following topics will be covered:
• Finite differences / finite volumes / finite elements / spectral methods
• transport schemes / semi-lagrangian methods
• splitting algorithms
• numerical diffusion/dispersion/anisotropy
• compressible flows
• turbulent flows
• boundary conditions
Prerequisites
An elementary knowledge of fluid dynamics will be assumed.
Evaluation
The evaluation of the course is done by a mid-term assignment and an end-of-course project in pairs.