Computational Methods for Large-Eddy Simulation in 2D Complex Geometries

Abstract

A method is described for the solution of the discrete Poisson equation in three dimensions, when one of the dimensions of the problem is periodic but the other two are of complex form. By utilising a direct Fourier method for the periodic dimension, the problem is reduced to a set of Helmholtz problems whose diagonal dominance increases with increasing wavenumber. The iterative solution of such problems on complex domains is shown to be highly efficient for the higher wavenumbers, and the use of multigrid acceleration for the lower wavenumber problems results in an effective overall solution procedure. Suitable line relaxation procedures and multigrid acceleration methods are described. The conditions under which the multigrid acceleration is beneficial are investigated, and the wavenumber range for which it should be activated is identified quantitatively. The method has applications in computational fluid dynamics and computational electromagnetics.