ECTS Credits: 6

Numerical methods for fluid dynamics
Emmanuel Dormy (DMA-ENS)

Numerical simulation is playing an expanding role in the study of fluid dynamics in scientific research. In this course, we will develop and analyse the various methods available to solve the partial differential equations relevant to computational fluid dynamics (elliptic, parabolic and hyperbolic). The emphasis will be placed on the algorithms and the convergence properties, as well as their application to a wide variety of problems in fluid dynamics.

• Overview of discretisation in time and space for pdes,

• Stokes equation and splitting algorithms,

• Transport schemes, numerical diffusion and dispersion,

• Compressible flows,

• Spectral methods and turbulent flows,

• Waves and numerical anisotropy,

• Open domains and boundary conditions,

• Complex domains,

• Prospects.