Vortex particle-mesh with combined immersed boundary and mesh refinement techniques : application to bluff-body and wake-vortex flows

The present work joins a global effort in the development of efficient and accurate numerical tools for the simulation of complex fluid flows. More specifically, we focus on unsteady external flows, a fluid dynamics discipline which actually pervades applied sciences and engineering. These are the flow encountered in aircraft or car aerodynamics, wind energy, biological locomotion, etc. In the problems addressed here, we assume that the flow is incompressible and that the inertial forces dominate the viscous stresses: we are dealing with both moderate and high Reynolds number flows. Furthermore, the present work treats the flow equations in a very distinct approach. We use a vortex particle-mesh (VPM) method, which belongs to the broader class of “vortex methods”. Such methods use the vorticity-velocity formulation of the Navier-Stokes equations, rather than the velocity-pressure formulation: the vorticity field is thus the primary variable. The major advantage comes from the compactness of the vorticity field for external flows and wakes. A limited number of particles is thus required to discretize the entire flow. First, an immersed boundary technique has been developed and adapted to capture the flow past arbitrary shape bodies. The motivation is to benefit from the enhanced efficiency provided by the VPM method in terms of computational cost (as shown in previous works). The required Poisson equation is solved using an efficient grid-based solver combined with a parallel fast multipole method (which provides the required boundary conditions on each subdomain). Second, an accurate approach handling hierarchically refined meshes has been developed. We use both grid patches and particles of varying resolution. The originality of this work is the combination of the handling of multiple flow resolutions together with a full 3-D VPM Navier-Stokes solver to compute incompressible flows. This method also benefits from the versatility of the parallel fast multipole method which enables the efficient solution of the Poisson equation and straightforward domain decomposition. We have also demonstrated the potential of the mesh refinement technique on a Large-Eddy Simulation of a turbulent vortex wake rollup at very high Reynolds number.(FSA 3) -- UCL, 201