Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations

摘要: Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries. A major part paper is devoted to development transform efficient in box geometries with periodic and free-slip boundary conditions. Techniques incorporating known symmetries invariances into illustrated Taylor-Green vortex. accurate representation rigid no-slip conditions also explained. class pseudospectral approximations introduced order handle more complicated dynamical interactions geometries. Later papers this series will demonstrate important advantages spectral over finite-difference many current interest present specific results various transition turbulent flows.