ABSTRACT
A majority of numerical schemes used in computational fluid dynamics are based on finite-difference methods. Since the variational formulation of a problem is essentially the global form of the associated conservation laws, finite-element methods automatically satisfy them. Since computational instability is associated with the violation of conservation laws (i.e., conservation of mean kinetic energy, mean vorticity, and mean square vorticity, called enstropy), it is less of a problem in finite-element methods. This chapter studies various time differencing schemes in combination with a number of finite elements and Arakawa’s difference schemes in space for their relative accuracy in amplitude and phase speed over long periods of integration. The effect of using ‘lumped mass’ and ‘consistent mass’ in the time approximation is also investigated.
