A High-Order Computational Framework for Wind Farm Modeling Using Flux Reconstruction and Actuator Disk Models

Abstract. This study focuses on implementing the Actuator Disk Model (ADM) in a high-order Flux Reconstruction (FR)/Correction Procedure via Reconstruction (CPR) framework to simulate Vertical Axis Wind Turbines (VAWTs). ADM applies body forces over a circular disk representing the turbine effects on fluid flows, instead of directly modeling turbine blades. This makes the simulation faster and more efficient while still capturing key flow physics, especially wake physics. A Gaussian filtering approach is used to ensure a smooth force distribution, which also helps blend the turbine forces naturally into the surrounding flow. The forces are applied to mesh elements marked as interface and solid cells, mimicking the effect of a real turbine. As a first step, source terms creating zero total drag and lift are used to represent an inviscid cylinder. Test results from the velocity and pressure fields show similar trends as those of the reference flow fields obtained from body-fitted mesh simulations. Extending to viscous flows at Re = 100 and Re = 1000, the ADM captures the expected vortex shedding patterns in the wake, consistent with body-fitted simulations and physical behavior. We envision that this method is useful for studying VAWT performance, wake interactions, and optimization of arrays of VAWTs.