Unsteady open boundaries for SPH using semi-analytical conditions and Riemann solver in 2D

Due to the Lagrangian nature of SPH, treating inlet/outlet boundaries (that are intrinsically Eulerian) is a challenging issue. An extension to the Unified Semi-Analytical boundary conditions is presented to deal with unsteady open boundaries in confined and free-surface flows. The presented method uses Riemann invariants to calculate flow properties near the open boundaries, thus allowing the possibility to treat complex shapes. Furthermore, details are presented for a parallel implementation of this method, including particle creation and deletion, updating properties of vertices and segments, and additional constraints on the time step. Simple validation cases are then displayed to illustrate the performance of the proposed method as well as the ability to deal with complex problems such as generation of water waves and free outlets.