The Euler equation of quasi-geostrophic fluids and volume preserving numerical methods

TL;DR

This paper investigates explicit volume-preserving numerical methods for the Euler equation of quasi-geostrophic fluids, emphasizing their impact on long-term simulations, statistical parameter estimation, and the importance of integral error monitoring.

Contribution

It introduces a framework for assessing volume-preserving discretizations in quasi-geostrophic fluid simulations and highlights the significance of integral errors in statistical parameter accuracy.

Findings

Statistical parameters depend on discretization integrals.

Errors in integrals affect parameter estimation despite volume preservation.

Monitoring integral errors can improve the reliability of long-term simulations.

Abstract

We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long simulations on an energy and enstrophy preserving discretization. To this purpose, we compute the average fields and estimate statistical parameters. It is observed that the statistical parameters depend on the integrals of the discretization and that the computed parameters are affected by the error in those, even if the volume of the phase space is correctly preserved. We conclude that monitoring the error in the integrals by the explicit volume preserving method can be used as an indication of how good the estimated parameters are.