Incompressible moving boundary flows with the finite volume particle method

Mesh-free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces. The finite volume particle method (FVPM) is a mesh-free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh-based finite volume method. Consequently, the method inherits many of the desirable properties of the classical finite volume method, including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms. In this paper, we describe the extension of FVPM to incompressible viscous flow with moving boundaries. An arbitrary Lagrangian–Eulerian approach is used, in conjunction with the mesh-free discretisation, to facilitate a straightforward treatment of moving bodies. Non-uniform particle distribution is used to concentrate computational effort in regions of high gradients. The underlying method for viscous incompressible flow is validated for a lid-driven cavity problem at Reynolds numbers of 100 and 1000. To validate the simulation of moving boundaries, flow around a translating cylinder at Reynolds numbers of 20, 40 and 100 is modeled. Results for pressure distribution, surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with FVPM results for an equivalent flow around a stationary cylinder. These results establish the capability of FVPM to simulate large wall motions accurately in an entirely mesh-free framework.