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

TL;DR

This paper introduces a 2.5D atmospheric model derived from 3D primitive equations, employing advanced numerical schemes to simulate mesoscale phenomena with validated physical accuracy.

Contribution

It presents a novel dimensional reduction and discretization approach for atmospheric equations, combining Discontinuous Galerkin and WENO-TVD schemes for improved numerical approximation.

Findings

Model accurately simulates mesoscale atmospheric phenomena

Discretization methods ensure numerical stability and physical validity

Validated through four representative test cases

Abstract

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 where 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 centered approach. We study four tests cases related to atmospheric phenomena to analyze the physical validity of the model.