# Arbitrarily high-order (weighted) essentially non-oscillatory finite difference schemes for anelastic flows on staggered meshes

## TL;DR

This paper introduces a high-order WENO finite difference scheme for simulating anelastic flows on staggered meshes, improving accuracy and robustness over existing methods.

## Contribution

The paper presents a novel arbitrarily high-order WENO scheme that combines ENO interpolations with WENO reconstructions for better accuracy on staggered grids.

## Key findings

- Demonstrates increased accuracy over existing schemes
- Shows improved robustness in numerical experiments
- Achieves high-order accuracy on staggered meshes

## Abstract

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily high-order accurate as it judiciously combines ENO interpolations of velocities with WENO reconstructions of spatial derivatives. A set of numerical experiments are presented to demonstrate the increase in accuracy and robustness with the proposed scheme, when compared to existing WENO schemes and state-of-the-art central finite difference schemes.