New Fast Wake Model Predicts Entire Wind Farm Flow at a Thousandth of the Cost

Wind farms are among the most consequential machines humanity has built, and yet the air moving through them remains surprisingly hard to simulate. Every spinning rotor leaves behind a turbulent, slowed-down wake that drifts downwind and slams into the turbines behind it, stealing energy and fatiguing blades. Predicting those wakes accurately has long forced engineers into an unhappy trade-off between speed and fidelity. Now, Frédéric Blondel of IFP Energies nouvelles and Majid Bastankhah of Durham University have unveiled a numerical scheme called FM-RANS that promises both at once, tracing the flow continuously from the moment air first feels a rotor’s pull to the far reaches of the wake, while slashing per-core computing costs by more than three orders of magnitude.

The work, published as a brief communication in the discussion-stage preprint series of the journal Wind Energy Science, addresses a stubborn gap in wind farm modeling. Full Reynolds-Averaged Navier-Stokes simulations, known as RANS, capture the physics of turbine wakes with respectable accuracy by solving averaged equations of fluid motion. But they are expensive. At the other end of the spectrum, engineering wake models run in milliseconds yet gloss over crucial details, particularly in the induction zone, the region upstream and around a rotor where the turbine begins decelerating and deflecting the incoming wind before it has even reached the blades. FM-RANS is designed to span that entire range in a single seamless calculation.

The key insight lies in how the new model handles pressure. Conventional parabolic RANS methods march the solution forward through the domain in the streamwise direction, which makes them dramatically faster than elliptic solvers that must iterate over the whole flow field simultaneously. The catch is that forward marching requires neglecting upstream pressure influences, and pressure gradients are precisely what shape the near-wake structure behind a turbine. In practice, modelers have patched this weakness with ad hoc near-wake corrections, bolting analytical fixes onto the numerics to fake the physics that was thrown away. Those corrections introduce discontinuities and tunable parameters that undermine confidence in the predictions.

Blondel and Bastankhah took a different route. Instead of discarding pressure physics and repairing the damage afterward, they coupled the parabolic marching framework with a recently developed analytical pressure-gradient formulation based on actuator disk theory. This analytical solution describes how the rotor imposes a pressure field on the flow, allowing the pressure gradient term to be reintroduced exactly where it matters, in the vicinity of the disk, without resorting to an expensive elliptic pressure solve. The result is a model that honors the physical mechanism of wake formation while retaining the raw speed of a forward-marching scheme.

The second pillar of the approach is turbulence closure, the mathematical recipe that tells the averaged equations how turbulent eddies mix momentum through the wake. Many fast wake models lean on oversimplified closures that cannot cope with the intense velocity gradients immediately downstream of a rotor, where wind speed can drop abruptly and shear is ferocious. FM-RANS instead adopts the k–ε–fp closure developed by van der Laan and colleagues, a variant of the classic two-equation turbulence model augmented with a correction term specifically calibrated for the steep gradients of turbine near-wakes. Choosing a closure that is genuinely suited to the flow regime, rather than merely convenient, is part of why the authors can dispense with near-wake corrections altogether.

The payoff is continuity. Where earlier parabolic models produced a patched-together picture, accurate far downstream but distorted near the rotor, FM-RANS yields a single smooth solution from the induction zone, through the near wake, into the far wake. That matters more than it might sound. The induction zone governs how much wind each turbine effectively intercepts and how it blocks its neighbors’ inflow in tightly packed arrays, while the far wake determines power losses hundreds of meters downwind. A model that captures both without seams lets engineers optimize layout, yaw strategies, and control schemes with consistent physics throughout the farm.

Validation focused on the toughest benchmark the authors could reasonably use as ground truth: full RANS simulations themselves. For an isolated turbine, FM-RANS closely reproduced the reference solutions for velocity deficit and turbulence across the entire wake. The test was then made harder with a column of four turbines, a configuration in which each rotor sits inside the compounded wakes of those upstream, and where small errors accumulate row by row into large discrepancies in the predicted power of the last machine. Again, the fast model tracked the full RANS results with very good agreement, suggesting that the analytical pressure closure retains the essential physics even in the interactive, multi-rotor environment of a real farm.

The performance figures are the headline grabber. Reducing per-core computational cost by more than three orders of magnitude means calculations that would monopolize a processor for hours on a RANS solver finish in seconds or minutes with FM-RANS. That changes the character of what wind farm analysis can be. Layout optimization, which might require evaluating tens of thousands of candidate turbine placements, or control studies exploring thousands of wake-steering yaw combinations, becomes tractable with a model that is physics-based rather than purely empirical. The authors are explicit that this is a proof of concept, presented as a brief communication, but the demonstrated combination of accuracy and speed is the kind of result that tends to reshape a subfield’s default toolkit.

The timing is propitious. Offshore wind is expanding into gigantic arrays where wake losses can reach double-digit percentages of annual energy production, and operators increasingly rely on dynamic wake steering, deliberately angling turbines to deflect their wakes away from downstream machines. Every such strategy depends on knowing where the wake goes and how it recovers, predictions that must be fast enough to run in real time and trustworthy enough to act on. A forward-marching RANS model with sound pressure physics could serve as the computational engine for such applications, sitting in the sweet spot between millisecond engineering formulas and hour-long high-fidelity solvers.

As with any preprint under open review, the findings will now face scrutiny from the community, with the discussion period open and the paper under consideration at Wind Energy Science. The authors note that one co-author sits on the journal’s editorial board, a disclosure handled under the journal’s standard transparency rules. Whether FM-RANS ultimately matures into an industry-standard tool will depend on extensions to three-dimensional terrain, atmospheric stability effects, and full farm scales. But the core demonstration stands: by pairing an elegant analytical description of rotor-induced pressure with a turbulence closure built for wakes, the model shows that the exhaustive and the instantaneous need not be enemies. The air through a wind farm, from first touch to final fade, may soon be simulated in one continuous, lightning-fast sweep.

Subject of Research: Fast parabolic RANS modeling of wind turbine induction zones and wakes in wind farm flows

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

Article References: Blondel, F., & Bastankhah, M. (2026). Brief communication: A fast parabolic RANS numerical model with analytical pressure closure for continuous induction-to-far-wake prediction in wind farm flows. https://doi.org/10.5194/wes-2026-172

Image Credits: AI Generated

DOI: 10.5194/wes-2026-172

Keywords: wind energy, wind farm wakes, RANS simulation, FM-RANS, turbulence closure, actuator disk, induction zone, parabolic model, wake modeling, computational fluid dynamics, k-epsilon model, offshore wind