Numerical simulations of incompressible flows in complex geometries.

摘要

A mainly spectral code along with domain-decomposition, a combination that is not widely in use in complex problems, has been developed for the solution of the 3-D unsteady incompressible Navier-Stokes equations. The code uses fully spectral or a combination of spectral-collocation and finite difference approximations and a 3-step splitting time-marching scheme. The developed Poisson solver utilizes matrix diagonalization and incorporates a direct sub-structuring method based on the influence matrix technique. As a first step, laminar and turbulent confined flows were simulated, initially with DNS, then with LES, using a modified Smagorinksi model. The domain-decomposition technique and parallel implementation were tested on the Poisson solver. The study focused on fluid flow phenomena and did not involve chemical reactions. We compared our calculations with numerical experiments performed on turbulent developed channel and pipe flow at Re_τ = 180. Annular flow, interesting but less popular, was also simulated. Finally we attempted to approach the problem of pipe flow with sudden expansion (confined jet) at low and moderate Reynolds numbers to investigate the ability of the code to handle complex geometries.