# Residual cross-grid flow numerical error in large-eddy simulations of cumulus-topped boundary layers

## TL;DR

This paper investigates how residual cross-grid flow errors in large-eddy simulations of cumulus-topped boundary layers depend on numerical scheme accuracy and domain translation velocity, revealing that higher-order schemes reduce these errors.

## Contribution

It identifies the cause of residual cross-grid flow errors as finite difference dispersion errors and demonstrates that increasing the order of accuracy diminishes these errors in LES.

## Key findings

- Residual cross-grid flow errors depend on numerical scheme accuracy.
- Higher-order schemes (up to sixth order) significantly reduce these errors.
- Domain translation velocity influences LES results due to dispersion errors.

## Abstract

A computational domain translation velocity is often used in LES simulations to improve computational performance by allowing longer time-step intervals. Even though the equations of motion are Galilean invariant, LES results have been observed to depend on the translation velocity. It is found that LES results of shallow convection depend on the domain translation velocity even when a Galilean invariant formulation is used. This type of model error is named residual cross-grid flow error, to emphasize the expectation that it should be negligible or zero. The residual gross-grid flow error is caused by biases in finite difference dispersion errors. Schemes with low resolving power (typically low order of accuracy) produce larger dispersion errors that can be amplified by large-scale flow asymmetries, such as strong updrafts in cumulus-cloud layers. Accordingly, the cross-grid flow error strongly depends on the order of accuracy of the numerical scheme progressively becoming negligible as the order of accuracy is increased from second to sixth in the present simulations.