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

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.