Simulation of unsteady flow around oscillating bluff bodies using a hybrid Eulerian Lagrangian scheme

Simulation of 2D, moderate-Reynolds-number flows around oscillating bluff bodies is performed using a multi-domain multi-method technique. The latter is based on decomposition of the computational domain into two regions: an Eulerian region surrounding the bluff body, and a Lagrangian region in the remainder of the flow. Within the Eulerian region, a second-order finite-difference discretization of the vorticity transport equation and the streamfunction Poisson equation is used. The resulting discrete equations are integrated using an alternating direction implicit (ADI) scheme. Meanwhile, a vortex element technique is used within the Lagrangian region. Vorticity is discretized into Lagrangian vortex elements of circular overlapping cores. The vortex elements are advected along particle trajectories, and their vorticity changes according to local diffusion fluxes which are computed using a conservative, deterministic particle exchange algorithm. Solutions within Eulerian and Lagrangian subdomains are joined along common boundaries using a coupling scheme which ensures continuity of the velocity and vorticity fluxes. The present construction combines the accuracy and flexibility of finite-difference methods with the efficiency of Lagrangian particle techniques. Implementation of the numerical scheme is discussed in light of results for rectangular bluff-body sections. Application of the simulations to compute unsteady aeroelastic forces and moments and to extract flutter derivatives is also discussed.