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

TL;DR

This paper develops a finite volume scheme for two-dimensional atmospheric primitive equations with topography, demonstrating improved accuracy near topography and analyzing effects of small-scale forcing on large-scale patterns.

Contribution

Introduces a projection-based finite volume scheme for 2D atmospheric equations with topography, reducing errors and enabling analysis of small-scale forcing effects.

Findings

Scheme shows good convergence with analytic solutions

Reduced errors near topography compared to standard schemes

Small-scale forcing induces large-scale pattern formation

Abstract

We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system of equations. In that respect, a version of a projection method is introduced to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. The resulting scheme allows for a significant reduction of the errors near the topography when compared to more standard finite volume schemes. In the numerical simulations, we first present the associated good convergence results that are satisfied by the solutions simulated by our scheme when compared to particular analytic solutions. We then report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated. The numerical results show that such a forcing is responsible for recurrent large-scale patterns to emerge in the temperature and velocity fields.