PHYSICS 716 / Incompressible Computational Fluid Dynamics

1.5 unit(s)

(same as part II of Mathematics *749)

We survey standard numerical methods for the solution of the incompressible fluid equations. Numerical properties of both the primitive (velocity-pressure) and non-primitive (stream function-vorticity) formulations analyzed. Particular attention is given to various discretization techniques, such as the use of staggered grids, explicit/implicit time-stepping and spectral approximation. Additionally, certain more advanced computational techniques will be mentioned, for instance, mesh generation in complicated domains, fast solvers (FFT, multigrid, wavelet) and high-order compact schemes. Approaches alternative to grid-based techniques such as Lagrangian particle methods will also be briefly introduced. Computer codes representing solution of some simple problems will be presented.