Delta Voronoi smoothed particle hydrodynamics, δ-VSPH

A Lagrangian scheme that combines Voronoi diagrams with smoothed particle hydrodynamics (SPH) for incompressible flows has been developed. Within the Voronoi tessellation, the Voronoi particle hydrodynamics (VPH) method is used, which is structurally similar to SPH. Two sub-domains are defined based on the proximity to the boundaries. The VPH formulation is used for particles close to solid boundaries, where SPH consistency and implementation of boundary conditions become problematic. Some overlapping of both sub-domains is allowed in order to provide a buffer zone to progressively transition from one method to the other. An explicit weakly compressible formulation for both sub-domains is used, with the diffusive term from the delta-SPH correction extended to the VPH formulation. In addition, the density field is periodically re-initialized and a shifting algorithm is included to avoid excessive deformation of the Voronoi cells. Solid, free-surface, and inlet/outlet boundary conditions are considered. A linear damping term is used during the initialization process to mitigate possible inconsistencies from the user-defined initial conditions. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks. (C) 2019 Elsevier Inc. All rights reserved.