An improved fringe-region technique for the representation of gravity waves in large-eddy simulation with application to wind farms

TL;DR

This paper introduces a novel fringe-region technique for large-eddy simulations that minimizes spurious gravity waves and improves inflow boundary condition accuracy in stratified atmospheric boundary layers, especially for wind farm modeling.

Contribution

A new fringe-region method that locally damps the vertical momentum to reduce spurious gravity waves in LES of stratified atmospheres.

Findings

The new method outperforms standard fringe-region techniques in various atmospheric states.

Tuned Rayleigh damping layer surpasses radiation conditions in boundary treatments.

Application to wind farm LES shows reflectivity as low as 0.75%.

Abstract

Large-eddy simulations of the atmospheric boundary layer are often performed using pseudo-spectral methods, which adopt a fringe-region approach to introduce inflow boundary conditions. However, we notice that a standard fringe-region technique excites spurious gravity waves when stratified atmospheres are considered, therefore enhancing the amount of energy reflected from the top of the domain and perturbing the velocity and pressure fields downstream. In this work, we develop a new fringe-region method that imposes the inflow conditions while limiting spurious effects on the surrounding flow. This is achieved by locally damping the convective term in the vertical momentum equation. We first apply the standard and wave-free fringe-region techniques to two-dimensional inviscid-flow simulations subjected to 169 different atmospheric states. A similar study is performed on a three-dimensional domain using a couple of atmospheric states. In all cases, the new fringe-region technique outperforms the standard method, imposing the inflow conditions with a minimal impact on the surrounding flow. Moreover, we also investigate the performance of two already existing non-reflective upper boundary conditions, that is a Rayleigh damping layer (RDL) and a radiation condition (RC). Results highlight the importance of carefully tuning the RDL to limit the distortion of the numerical solution. Also, we find that the tuned RDL outperforms the RC in all cases. Finally, the tuned RDL together with the wave-free fringe-region method are applied to an LES of a wind farm operating in a conventionally neutral boundary layer, for which we measure a reflectivity of only 0.75%.