Fast Multipole Integration into Rotor Simulations with State-Space Vortex Particle Wake

This work presents a novel computational framework that integrates the fast multipole method (FMM) into a coupled panel and vortex particle method (VPM), developed in state-variable form, to significantly improve the efficiency and scalability of aerodynamic simulations. The approach utilizes panel methods to model wing or blade surfaces and their near wake, while vortex particles are employed to capture far wake dynamics, enabling a detailed and accurate representation of the flowfield. The coupled dynamics are formulated as a system of ordinary differential equations, which are both self-contained and inherently linearizable, facilitating seamless integration with flight dynamics and control analysis. To overcome the computational challenges associated with large-scale simulations, the FMM is incorporated to approximate particle–particle interactions efficiently, reducing the computational complexity from [Formula: see text] to [Formula: see text] while limiting the loss in accuracy to less than 1%. The improved solver, developed using MATLAB ® , is utilized to model the aerodynamic performance of a rotor blade in hover conditions. The code is verified against experimental data for the hover case, showing acceptable agreement in the blade load distribution and demonstrating the solver’s reliability. Results also demonstrate significant improvements in computational performance and scalability, showcasing the framework’s capability to handle simulations involving large numbers of particles. The study further examines key FMM parameters, in particular the truncation order ([Formula: see text]) and the number of octree levels ([Formula: see text]), to optimize the tradeoff between accuracy, computational cost, and memory requirements. By integrating FMM with a state-space formulation of coupled panel and vortex particle methods, this work establishes an efficient and scalable solver for aerodynamic analysis.