Coupling a vortex particle-mesh method for compressible flows with a discontinuous Galerkin solver

Many flow problems involve the wakes of devices, which may have a significant impact on a downstream device. For instance, the large-scale vortices generated by an airplane may constitute a significant hazard if they are encountered by another aircraft; the interactions between the vortices shed by a helicopter blade with the following blade contribute to complex and fatigue-inducing loadings on the rotor; this is also an issue for a Counter-Rotating Open Rotor (CROR). Accurate numerical simulations of such physics entail a twofold effort: first, the efficient capture of the complex aerodynamics in the region close to the body and, second, the advection of coherent structures until the interaction with another device. Eulerian methods constitute an efficient tool to study near-wall phenomena as they allow a highly anisotropic resolution. Nevertheless, the associated cost when trying to also capture the wake turbulence and vortices over a large distance downstream is prohibitive. A hybrid approach is here proposed to address this challenge: an Eulerian solver is coupled with a “Vortex Particle-Mesh” (VPM) solver, which is well suited to capture advection-dominated flows in unbounded domains. First, a VPM method for compressible flows is developed. Indeed, existing VPM solvers are mainly designed to study incompressible flows whereas the problems addressed here require accounting for compressibility effects. A Brinkman penalization technique is also adapted in order to account for obstacles. Then, the VPM solver is coupled to a high-order Discontinuous Galerkin solver responsible for the near-body region. The potential of the methodology is demonstrated on benchmark test cases.