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Numerical methods for fluid dynamics
The numerical resolution of fluid dynamics equations is becoming increasingly important in many aspects of scientific research. In this course, we will develop and analyze the methods used to solve the partial differential equations relevant to fluid dynamics (elliptic, parabolic and hyperbolic).
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.