High-order well-balanced finite-volume schemes for barotropic flows. Development and numerical comparisons

TL;DR

This paper compares classical and high-order finite-volume schemes for barotropic ocean flows, evaluating their accuracy, stability, and boundary condition handling, with application to eddy formation in Norwegian shelf jets.

Contribution

It introduces a comparison between finite-difference and high-order finite-volume schemes for barotropic flows, highlighting their performance differences and applicability.

Findings

High-order schemes improve accuracy in simulating eddy formation.

Both schemes effectively capture mesoscale eddies caused by flow instability.

Boundary condition treatment significantly impacts simulation stability.

Abstract

In this paper we compare a classical finite-difference and a high order finite- volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary conditions. We apply the schemes to the problem of eddy formation in shelf slope jets along the Ormen Lange section of the Norwegian shelf. Our results strongly confirm the development of mesoscale eddies caused by instability of the flows.