A new open boundary formulation for incompressible SPH

In this work a new formulation for inflow/outflow boundary conditions in an incompressible Smoothed Particles Hydrodynamics (ISPH) model is proposed. It relies on the technique of unified semi-analytical boundary conditions that was first proposed for wall boundary conditions in 2013, then extended to open boundaries in the framework of weakly-compressible SPH (WCSPH). An ISPH model relying on that formulation for solid boundaries was then proposed, which is the one considered here. It includes a buoyancy model for temperature effects and a k−ϵ turbulence closure. There are two main requirements for the imposition of open boundaries in ISPH: an algorithm to let particles enter and leave the domain, and the correct imposition of open boundary conditions on the fields. Regarding the algorithm for particles creation/destruction, it relies on the variation of mass of the particles located at the open boundaries. When the mass of such a particle reaches a threshold, a new particle is released. On the other hand, the imposition of open boundary conditions on the fields is done by prescribing the value of the boundary terms appearing in the semi-analytical formulation. The formulation was first validated in 2-D on a cut dam-break, a case of propagation of a solitary wave and a Creager weir. It was then extended to 3-D and tested on a 3-D circular pipe. A preliminary application case consisting of two connected pipes at different temperatures was then simulated. The results are promising since in all cases the fluid enters and leaves the domain as prescribed and generating none or very few reflected waves.