A weak coupling between a near-wall Eulerian solver and a Vortex Particle-Mesh method for the efficient simulation of 2D external flows

We introduce and validate a weak coupling approach between a body-fitted velocity-pressure solver and a Vortex Particle-Mesh (VPM) method in 2D for the simulation of incompressible external aerodynamics. The approach does not involve inner iterations, conserves circulation up to interpolation accuracy without resorting to a panel method, and accommodates different time steps across the solvers. It also utilizes a mixed boundary condition for the body-fitted solver that ensures the continuity of the vorticity field across the solvers. The second order convergence of the methodology is first demonstrated. We then assess it on the flow past a cylinder at various Reynolds numbers (from Re=550 to 9500), and we finally apply it to the flow past an airfoil at Re=5000