Fast Multipole Method for a Rotor Simulation With a State-Space Vortex Particle Method

This study presents the integration of the Fast Multipole Method (FMM) into a coupled panel and vortex particle method (VPM), formulated in state-variable form, to enhance computational efficiency and scalability for aerodynamic simulations. Panels are utilized to model the surface of the wings or blades and the near wake, while vortex particles are used to represent the far wake dynamics, providing a detailed and comprehensive representation of the flow field. The coupled dynamics are expressed as a system of ordinary differential equations that are self-contained and inherently linearizable, offering a framework for dynamic analysis and control system design. The FMM is subsequently incorporated to efficiently approximate particle-particle interactions, addressing computational challenges associated with large-scale simulations. The enhanced solver, implemented in MATLAB®, is applied to simulate the aerodynamics of a rotary wing in hover, demonstrating its ability to improve both performance and scalability. By integrating the FMM, the computational complexity of particle-particle interactions is reduced from O (N 2 ) to O (Np), while maintaining an acceptable level of accuracy, enabling the simulation of systems with large numbers of particles. Selection of key FMM parameters such as the truncation order (P) and the number of levels (L), is investigated to balancing accuracy, computational efficiency, and memory usage. This integration establishes a foundation for future advancements in aerodynamic solvers, enhancing their applicability to large-scale rotorcraft simulations.