Computational study of numerical flux schemes for mesoscale atmospheric flows in a Finite Volume framework

TL;DR

This paper develops a finite volume density-based numerical scheme for non-hydrostatic atmospheric flows, incorporating hydrostatic reconstruction and comparing four Riemann solvers through benchmark tests.

Contribution

It introduces a density-based finite volume approach with hydrostatic balancing for atmospheric flows and evaluates four Riemann solvers in this context.

Findings

The approach maintains well-balanced solutions during simulations.

HLLC-AUSM performs best among the tested Riemann solvers.

The method accurately captures thermal bubbles and density currents.

Abstract

We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe non-hydrostatic atmospheric flow. The well-balancing of the approach is ensured by a local hydrostatic reconstruction updated in runtime during the simulation to keep the numerical error under control. To approximate the solution of the Riemann problem, we consider four methods: Roe-Pike, HLLC, AUSM+-up and HLLC-AUSM. We assess our density-based approach and compare the accuracy of these four approximated Riemann solvers using two two classical benchmarks, namely the smooth rising thermal bubble and the density current.