Local Uniform Stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow.