High-order finite volume schemes for layered atmospheric models

TL;DR

This paper introduces a high-order finite volume numerical scheme for layered atmospheric models, combining layering techniques with ADER schemes to efficiently simulate atmospheric phenomena at high horizontal resolution.

Contribution

It develops a novel layered modeling approach with high-order ADER schemes, enabling efficient and accurate simulation of atmospheric models with mixed resolution requirements.

Findings

The scheme achieves convergence in 2D linear advective models.

Layering based on Galerkin discretizations improves vertical resolution.

Higher horizontal order enhances simulation accuracy.

Abstract

We present a numerical scheme for the solution of a class of atmospheric models where high horizontal resolution is required while a coarser vertical structure is allowed. The proposed scheme considers a layering procedure for the original set of equations, and the use of high-order ADER finite volume schemes for the solution of the system of balance laws arising from the dimensional reduction procedure. We present several types of layering based upon Galerkin discretizations of the vertical structure, and we study the effect of incrementing the order of horizontal approximation. Numerical experiments for the computational validation of the convergence of the scheme together with the study of physical phenomena are performed over 2D linear advective models, including a set of equations for an isothermal atmosphere.