A weak coupling between a Near-Wall Eulerian solver and a Vortex Particle-Mesh method for the efficient simulation of 3D incompressible external flows.*

We report on a new hybrid numerical method for the simulation of 3D incompressible external flows, coupling a Near-Wall (NW) Eulerian solver, Nek5000, with a Multi-Resolution Vortex Particle-Mesh (VPM) solver, Murphy.

The NW Eulerian solver is restricted to a body-fitted mesh spanning the close vicinity of the body. It uses the velocity-pressure formulation of the N-S equations and allows the accurate capture of the fine-scales boundary layer phenomena. The VPM solver is based on the vorticity-velocity formulation of the N-S equations and uses a mesh encompassing the whole numerical domain. The advantages of the Vortex Particle method are leveraged to capture the advection of the wake vortical structures up to far downstream.

Both solvers are weakly coupled. The NW solver transfers the shed vortical structures to VPM through a volumetric coupling, while VPM imposes mixed boundary conditions on the outer surface of the NW solver. This method guarantees the continuity of the vorticity field at the interface between both solvers and a conservation of the circulation. We present the validation of the solver using a DNS of a low-Reynolds number aerodynamic testcase such as the flow past a cylinder with periodic spanwise boundary conditions. The continuity of the vorticity field is assessed, aerodynamic forces are measured and the vortical structures in the wake are analyzed.