The double-tree method: An O(n) unsteady aerodynamic lifting surface method

Two new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time-saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n log n) tree methods together results in an O(n) method, called the double-tree method. Other case studies show that the trade-off between accuracy and speed can be easily and reliably controlled by the agglomeration cut-off distance. For a flat plate with 5x200 panels analysed over 20 time steps, the double-tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full-aircraft analysis within optimisation or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.