A Mixed Formulation Vorticity-Velocity Solver using AMReX Framework for Wind Farm Modeling

This paper presents the development of a hybrid numerical framework for coupling a compressible, velocity-based Computational Fluid Dynamics solver (CGE) with an incompressible, vorticity-based solver (VorTran-M2-AMR) that can be applied for modeling wind farms. The methodology employs an efficient buffer-region treatment with a tailored vorticity/velocity information transfer strategy to meet two key requirements: a) robust and accurate projection of velocity and vorticity fields across the two solver interfaces, and b) preservation of physical flow features while minimizing spurious artifacts in the coupled domain. With the proposed approach, only a limited amount of information is required to be transferred between the two solver domains. A baseline configuration of laminar flow past a cylinder is used to assess multiple aspects of the coupling procedure in detail. From this assessment, it is found that the off-body vorticity and velocity fields generated by VorTran-M2-AMR exhibit strong agreement with the CGE solution, and that the hybrid method accurately captures expected physical behavior, including velocity discontinuities and far-field vorticity transport. The framework is then applied to more complex and practically relevant scenario of a startup vorticity evolution from an impulsively started wing. For these cases, the coupling demonstrates scalability, consistency at the interface, and improved computational efficiency while preserving fidelity in regions of interest. In future, the proposed hybrid framework will be extended to wind-farm–scale simulations involving multiple wind turbines. Each turbine will be resolved in its own CFD subdomain, embedded within a larger VorTran-M2 domain to efficiently capture wake evolution and turbine–turbine interactions across the farm.