Acceleration of unsteady vortex lattice method via dipole panel fast multipole method

Abstract The Unsteady Vortex Lattice Method (UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most time-consuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O N 2 , we present an O N Dipole Panel Fast Multipole Method (DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P . Two methods (the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments (with three harmonics), DPFMM is approximately two times faster for N ∈ [ 10 3 , 10 6 ] . The simulation time of a multirotor ( N ∼ 10 4 ) is reduced from 100 min (with unaccelerated direct solver) to 2 min (with DPFMM).