A strongly coupled Eulerian Lagrangian method verified in 2D external compressible flows

Abstract

A hybrid solver for external compressible flows is formulated by combining a standard finite volume Eulerian CFD solver with a Lagrangian (particle) one. The Eulerian domain is confined close to the solid boundaries and may be split in separate disjoint subsets. The Lagrangian domain covers the entire domain while the flow is represented by particles that carry complete flow information defined by mass, dilatation, vorticity and pressure. The Lagrangian part couples the two solvers by providing the outer boundary conditions to the Eulerian grid. On the other hand, the Eulerian solver communicates the presence of walls to the Lagrangian one, by updating the particle flow properties close to them. The formulation is completed by combining Helmholtz’s decomposition with the Particle Mesh technique which determines the velocity field that transports the particles, provides accurate outer boundary conditions for the Eulerian solver and decisively reduces the computational cost. In the present paper the inviscid flow around a NACA 0012 airfoil is considered from low to high subsonic conditions in steady and pitching mode. Hybrid predictions are compared to standard CFD results and verification of the proposed solver is carried out. The comparison shows that, if shocks are included in the Eulerian grid of the hybrid solver, the loads are accurately estimated, and that for the same resolution, the numerical diffusion in the wake is substantially reduced.