Spectral method for vorticity-streamfunction equations, with application to Rayleigh-Benard convection

Abstract

The spectral method with an explicit time integration scheme is implemented to solve the vorticity-streamfunction equations. In spectral method, functions are approximated with finite sums of periodic sine and cosine functions, which makes this method suitable for periodic problems. Numerical experiments for several cases are discussed. In Rayleigh-Benard convection problem, a horizontal layer of incompressible fluid is kept within high and low temperatures along the bottom and top boundaries, respectively. Triggered by a periodic initial condition, we simulate the occurrence of a regular pattern of convection cells, known as Benard cells.