The suite of Taylor–Galerkin class schemes for ice transport on sphere implemented by the INMOST package

Realizations of the numerical solution of the scalar transport equation on the sphere, written in divergent form, are presented. Various temporal discretizations are considered: the one-step Taylor–Galerkin method (TG2), the two-step Taylor–Galerkin method of the second (TTG2), third (TTG3), and fourth (TTG4) orders. The standard Finite-Element Galerkin method with linear basis functions on a triangle is applied as spatial discretization. The flux correction technique (FCT) is implemented. Test runs are carried out with different initial profiles: a function from C ∞ (Gaussian profile) and a discontinuous function (slotted cylinder). The profiles are advected by reversible, nondivergent velocity fields, therefore the initial distribution coincides with the final one. The case of a divergent velocity field is also considered to test the conservation and positivity properties of the schemes. It is demonstrated that TG2, TTG3, and TTG4 schemes with FCT applied give the best result for small Courant numbers, and TTG2, TTG4 are preferable in case of large Courant number. However, TTG2+FCT scheme has the worst stability. The use of FCT increases the integral errors, but ensures that the solution is positive with high accuracy. The implemented schemes are included in the dynamic core of a new sea ice model developed using the INMOST package. The acceleration of the parallel program and solution convergence with spatial resolution are demonstrated.

MODELLING THE HYDROTHERMODYNAMICS OF THE SURFACE LAYER OF A STRATIFIED TROPICAL SUBTROPICAL OCEAN

In the present paper a two-layer model is developed for the non-permanent hydrothermodynamics of a tropical subtropical coastal ocean. The model includes the equations of motion, continuity and heat. The equations apply only to the thin and warm oceanic surface layer. The deep layer is stipulated to be motionless, arbitrarily deep and separated from the upper layer by a density discontinuity. Cold deep water is carried across the interface from the lower into the upper layer; it is warmed up there by the net energy input from the atmosphere into the ocean The non-uniform sea surface wind stress and heat at the surface are the main forcing functions of the model. A numerical finite element method is proposed to approximate the hydrothermodynamic problem. The model uses simple linear spatial and temporal continuous polynomial and a stabilizing Petrov-Galerkin operator to improve the classical finite element Galerkin method. The hydrothermodynamic response is obtained for the eastern pacific boundary in the southern hemisphere. Monthly climatological data are used to determine the wind and heat fluxes forcings of the model. The main features of the observed Sea Surface Temperature (SST) pattern are successfully simulated by the model. In particular the predicted : upwelling along the coastal boundary; warm water intrusion in offshore side and signals of countercurrents are in a quite good agreement with observations.