Numerical Method
This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. The approach involves updating for the vorticity first and then solving for the fluid velocity each time step. The chapter continues with a discussion of two very different spatial discretizations, whereby the vertical derivatives are approximated with a finite-difference method and the horizontal derivatives with a spectral method. The nonlinear terms are computed in spectral space. The chapter also considers the Adams-Bashforth time integration scheme and explains how the Poisson equation can be solved at each time step for the updated streamfunction given the updated vorticity.