An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement

TL;DR

This paper introduces an efficient IMEX-DG solver with adaptive mesh refinement for atmospheric simulations, enabling accurate modeling of compressible flows in low Mach regimes with improved computational efficiency.

Contribution

The paper develops a novel IMEX-DG solver with adaptive mesh refinement tailored for atmospheric dynamics, combining high accuracy and efficiency for compressible flow simulations.

Findings

Demonstrates improved accuracy on classical atmospheric benchmarks

Shows efficiency gains through adaptive mesh refinement

Validates suitability for low Mach regime simulations

Abstract

We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based on an $h-$adaptive Discontinuous Galerkin spatial discretization and on a second order Additive Runge Kutta IMEX method for time discretization, especially designed for low Mach regimes. The solver is implemented in the framework of the $deal.II$ library, whose mesh refinement capabilities are employed to enhance efficiency. A number of numerical experiments based on classical benchmarks for atmosphere dynamics demonstrate the properties and advantages of the proposed method.