Modeling and numerical approximation of a 2.5D set of equations for mesoscale atmospheric processes

The set of 3D inviscid primitive equations for the atmosphere is dimensionally reduced by a Discontinuous Galerkin discretization in one horizontal direction. The resulting model is a 2D system of balance laws with a source term depending on the layering procedure and the choice of coupling fluxes, which is established in terms of upwind considerations. The “2.5D” system is discretized via a WENO–TVD scheme based in a flux-limiter approach. We study four tests cases related to atmospheric phenomena to analyze the physical validity of the model.