A new element for local refinement in the non-lineal and unsteady vortex-lattice method

It is very well known that the non-lineal and unsteady vortex-lattice method (UVLM) produces better results when the vortex sheets, that simulate the boundary layer on the body and the free wakes, are discretized using uniform rectangular vortex-rings elements, producing structured lattices (or meshes). Moreover, the density of elements on these grids strongly affect the accuracy of the numerical simulations. So far, global mesh refinement is the only mechanism known to improve the precision of such results. In this article, a modified and enlarged version of the UVLM is presented, which admits local mesh refinement of the body bound-vortex lattice by the introduction of a set of new elements, called transition elements. Using these elements, it is possible to reduce the size of the vortex lines on specific areas of the vortex lattice in order to improve the accuracy of the results, while keeping larger vortex lines in the rest of the discretized bound-vortex sheet. The lattice, refined in this way, allows a significant reduction of the computational costs. The method developed was successfully validated by contrasting against previously published test cases.