A comparison of operator splitting and approximate matrix factorisation for the shallow water equations in spherical geometry

The shallow water equations (SWEs) in spherical geometry provide abasic prototypefor developing and testing numerical algorithms for solving the horizontaldynamics in global atmospheric circulation models. When solving the SWEs on a global fine uniform lat-lon grid, an explicit timeintegration method suffers from a severe stability restriction on theadmissible step size. In a previous paper, we investigated an A-stable,linearly-implicit, third-order time integration method (Ros3), which wecombinedwith approximate matrix factorization (AMF) to make it cost-effective. Inthis paper, we further explore this method and we compare itto a Strang-type operator splitting method. Our main focus is on the localerror of the methods, their numerical dispersion relation and their accuracyand efficiency when applied to the well-known SWEs test set. Thecomparison shows that Ros3with AMF accurately presents both low and mid frequency waves. Moreover,Ros3 with AMF makes a good candidate for theefficient solution of the SWEs on a global fine lat-longrid. In contrast, Strang splitting is not advocated, in view of itsinaccuracy in the polar area and the resulting inefficiency.