The actuator line method (ALM) is extensively used in wind turbine and rotor
simulations. However, its original uncorrected formulation overestimates the
forces near the tip of the blades and does not reproduce well forces on
translating wings. The recently proposed vortex-based smearing correction for
the ALM is a correction based on physical and mathematical properties of the
simulation that allows for a more accurate and general ALM. So far, to correct
the forces on the blades, the smearing correction depended on an iterative
process at every time step, which is usually slower, less stable and less
deterministic than direct methods. In this work, a non-iterative process is
proposed and validated. First, we propose a formulation of the non-linear
lifting line that is equivalent to the ALM with smearing correction, showing
that their results are practically identical for a translating wing. Then, by
linearizing the lifting line method, the iterative process of the correction is
substituted by the direct solution of a small linear system. No significant
difference is observed in the results of the iterative and non-iterative
corrections, both in wing and rotor simulations. Additional contributions of
the present work include the use of a more accurate approximation for the
velocity induced by a smeared vortex segment and the implementation of a
free-vortex wake model to define the vortex sheet, that contribute to the
accuracy and generality of the method. The results present here may motivate
the adoption of the ALM by other communities, for example, in fixed-wing
applications.Comment: 30 pages, 9 figure