A coupled overset vorticity transport and compressible Euler solver for vortex-dominated flows

An efficient solver for the incompressible vorticity transport equations on adaptive Cartesian grids is coupled to an unstructured spectral volume solver for the conservative form of the compressible Euler equations using overset grid assembly and interpolation provided by SUGGAR and DiRTlib, respectively. Vortical flow structures originate at solid surfaces in near-body regions employing the Euler solver and are transported into the wake region that employs an Eulerian Vorticity Transport (EVT) solver. The excessive numerical dissipation common to most grid-based Navier-Stokes solvers is avoided in the wake region by solving the fluid dynamic equations in vorticity conservation form. In addition, the adaptive Cartesian mesh utilized in the wake region allows for efficient transport and preservation of vortical structures by means of localized adaptive mesh refinement and coarsening. Two different approaches for evaluating the EVT velocity field, one involving a fast summation technique based on the Cartesian Treecode method, and the other utilizing a multigrid Poisson approach, are presented and compared. The implementation of both the solution algorithm and overset coupling methodology is described in detail, and results for several different test cases are presented which demonstrate the effectiveness of the hybrid EVT-Euler simulation capability for accurately transporting vortical structures between a near-body compressible Euler solver and an off-body EVT solver.