The ability to accurately and rapidly assess unsteady interactional aerodynamics is a shortcoming and bottleneck in the design of various next-generation aerospace systems: from electric vertical takeoff and landing (eVTOL) aircraft to airborne wind energy. In this doctoral work, we present a novel computational fluid dynamics (CFD) scheme based on a reformulated vortex particle method (rVPM) for the analysis of complex interactional aerodynamics. The rVPM is a meshless large eddy simulation (LES) solving the LES-filtered Navier-Stokes equations in their vorticity form. It uses a Lagrangian scheme, which not only avoids the hurdles of mesh generation, but it also conserves vortical structures over long distances with minimal numerical dissipation while being orders of magnitude faster than conventional mesh-based CFD. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures where the predominant cascade mechanism is vortex stretching. Extensive validation is presented, asserting the scheme as a meshless LES that accurately resolves large-scale features of turbulent flow and showing our meshless LES to be 100x faster than a mesh-based LES with similar fidelity. To conclude, the capabilities of the framework are showcased through the simulation of a tiltwing eVTOL vehicle as it transitions from powered lift to wing-borne flight, featuring rotors with variable RPM, tilting of wings and rotors, and complex aerodynamic interactions.