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

Abstract

Due to the Lagrangian nature of SPH, treating inlet/outlet boundaries (that are intrinsically Eulerian) is a challenging issue. An extension to the Unified SemiAnalytical 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.

On the state-of-the-art of particle methods for coastal and ocean engineering

“…The vortex formation patterns were studied for Froude numbers in between 0.3 and 2.0, based on the diameter, and for submergence-diameter ratios in between -0.5 and 2.5. Ferrand et al [2017] presented an extension to the unified semi-analytical boundary conditions for SPH with Riemann solver for setting the unsteady open boundaries with complex shapes in confined and free-surface flows. The method was validated in simulation of water waves generation and free outlets.…”

Mixture model for two-phase flows with high density ratios: A conservative and realizable SPH formulation

“…In this operator, the renormalization factor γ a presented in Ferrand et al (2017) was used to account for potential truncated kernel supports near boundaries:…”

“…where Ω a denotes the kernel support of the particle a. Moreover, following Ferrand et al (2017), the contributions to the gradient of γ are:…”

“…where n s is the inward unit normal to the boundary segment s. These values can be computed analytically as explained in Ferrand et al (2017).…”

“…• The first term of the right hand side of equation ( 32) can be identified as the first term of equation ( 33) using the relation ( 25). The computation of the temporal derivative of the total volume relies on the use of an exact time integration scheme, following what is suggested by Ferrand et al (2017). It proves to be better at simulating the mixture at rest (the usual continuity equation resolution with antisymmetric divergence led to spurious convection cells which appeared to be linked to the accumulation of numerical errors).…”