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We aim to study a finite volume scheme to solve the two dimensional inviscidprimitive equations of the atmosphere with humidity and saturation, in presenceof topography and subject to physically plausible boundary conditions to thesystem of equations. In that respect, a version of a projection method isintroduced to enforce the compatibility condition on the horizontal velocityfield, which comes from the boundary conditions. The resulting scheme allowsfor a significant reduction of the errors near the topography when compared tomore standard finite volume schemes. In the numerical simulations, we firstpresent the associated good convergence results that are satisfied by thesolutions simulated by our scheme when compared to particular analyticsolutions. We then report on numerical experiments using realistic parameters.Finally, the effects of a random small-scale forcing on the velocity equationis numerically investigated. The numerical results show that such a forcing isresponsible for recurrent large-scale patterns to emerge in the temperature andvelocity fields.

Numerical weather prediction in two dimensions with topography, using a finite volume method