A Hybrid High-Order Vorticity-Based Eulerian and Lagrangian Vortex Particle Method, the 2-D Case

Hybrid Lagrangian-Eulerian solvers combine the convective and compactness advantages of vortex methods with the spatial anisotropy and boundary-resolving advantages of Eulerian methods to create flexible solvers capable of adequately capturing thin boundary layers while still maintaining wake vortex coherency for unsteady incompressible flow in complex geometries. The present paper details a new hybrid method which combines, in one open-source package, a novel, compact, high-order Eulerian scheme for vorticity transport to predict the flow in the near-boundary region with a grid-free, unremeshed, Lagrangian Vortex Particle Method (LVPM) for the off-boundary vorticity-containing region. This paper focuses on the hybridization of the two methods and demonstrates its effectiveness on two canonical benchmarks: flow in 2-D lid-driven cavity at Re = 1,000 and impulsively started flow over a circular cylinder at Re = 9,500. In each case, the hybrid method improves upon a pure LVPM and uses far fewer cells than a purely Eulerian scheme. In addition, the size of the associated Eulerian region is greatly reduced compared to previous hybrid methods.