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

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 without altering the flow downstream. 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 imposes the inflow conditions without altering the surrounding flow. Moreover, we also investigate the performance of two 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 0.7%.

Large-eddy simulations of the interaction between wind farms and mesoscale effects

“…However, the numerical investigation of wind farm induced gravity waves requires a large numerical domain length, width and height to prevent domain e ects. When applying inflow methods, such as the concurrentprecursor method, domain-induced gravity waves might be generated in stable ABLs, which can a ect the velocity and pressure fields drastically [261]. The recently developed fringe-region technique by Lanzilao and Meyers [261] shows promising results in reducing gravity waves that are triggered by the numerical domain.…”

“…When applying inflow methods, such as the concurrentprecursor method, domain-induced gravity waves might be generated in stable ABLs, which can a ect the velocity and pressure fields drastically [261]. The recently developed fringe-region technique by Lanzilao and Meyers [261] shows promising results in reducing gravity waves that are triggered by the numerical domain. Thus, interesting studies on gravity waves triggered by wind farms, varying the distances in between the wind farms and the atmospheric conditions, can be performed in future works.…”