Wave analysis for different splittings of the shallow water equations on the β-plane

AbstractThe effects of operator splitting on the wave solutions of the linearized shallow water equations have been investigated in [Á. Havasi, Dispersion analysis of operator splittings in the linearized shallow water equations, in: I. Lirkov, S. Margenov, J. Wasniewski (Eds.), Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6–10, 2005, in: Lecture Notes in Computer Science, vol. 3743, Springer, 2006] by directional decomposition of the sub-operators and by the constant Coriolis parameter f. This–so-called f-plane–approximation does not allow the formation of Rossby waves, which play a major role in the evolution of midlatitude weather systems. In this paper we apply β-plane approximation in the shallow water equations and examine how the resulting Rossby-gravity waves are influenced by the separation of different physical effects in some concrete splitting schemes

On the numerical solution of the three-dimensional advection-diffusion equation

A new approach is proposed for the numerical solution of three-dimensional advection-diffusion equations, which arise, among others, in air pollution modelling. The technique is based on directional operator splitting, which results in one-dimensional advection-diffusion equations. Then upstream-type difference approximations are applied for the first-order derivatives and non-standard difference approximations for the second-order derivatives. This approach leads to significant qualitative improvements in the behaviour of the numerical solutions