Preprints
https://doi.org/10.5194/wes-2026-172
https://doi.org/10.5194/wes-2026-172
14 Oct 2026
 | 14 Oct 2026
Status: this preprint is currently under review for the journal WES.

Brief communication: A fast parabolic RANS numerical model with analytical pressure closure for continuous induction-to-far-wake prediction in wind farm flows

Frédéric Blondel and Majid Bastankhah

Abstract. Parabolic Reynolds-Averaged Navier-Stokes (RANS) approaches offer an attractive compromise between the accuracy of RANS and the efficiency of analytical methods. However, due to neglecting pressure gradients, these models often require near-wake corrections. Moreover, they are typically based on over-simplistic turbulence closures. To address these limitations, this brief proof of concept couples a recently developed analytical pressure-gradient formulation (Bastankhah et al., 2026) with a parabolic RANS framework. It also uses the k − ε − fp turbulence closure, well suited to strong near-wake velocity gradients (van der Laan et al., 2015). The model closely reproduces RANS results, while reducing per-core computational costs by more than three orders of magnitude.

Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.

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Frédéric Blondel and Majid Bastankhah

Status: open (until 11 Nov 2026)

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Frédéric Blondel and Majid Bastankhah
Frédéric Blondel and Majid Bastankhah
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Short summary
This brief communication introduces FM-RANS, a parabolic (forward-marching) RANS model for wind farm flows that couples an analytical actuator-disk pressure-gradient solution with the k−ε−fp turbulence closure. This allows continuous prediction from the induction zone through the far wake without near-wake corrections. Compared with RANS for single turbines and four-turbine columns, it shows very good agreement while reducing per-core computational costs by more than three orders of magnitude.
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