Parallel Godunov smoothed particle hydrodynamics (SPH) with improved treatment of Boundary Conditions and an application to granular flows

Smoothed Particle Hydrodynamics has been successfully used for various fluid-dynamics problems, such as breaking-waves, flooding etc., since it was originally proposed. While the Lagrangian approach is naturally suitable for free-surface flows, enforcing boundary conditions and poor approximations in the presence of discontinuities in the solution are major difficulties with the method. In this paper we present an enhanced conservative Godunov SPH based on the work of Inutsuka [S. Inutsuka, Reformulation of smoothed particle hydrodynamics with Riemann solver, Journal of Computational Physics 179 (2002) 238-267] that accurately resolves discontinuities without the need to use artificial viscosity, preserves partition of unity everywhere in the domain, correctly and flexibly enforces necessary essential and frictional slip boundary conditions to approximately solve free-surface granular flows. The development is motivated by the need to improve upon depth averaged grid based models of large scale debris flows and avalanches often characterized as granular flows. Simple validation of the results is obtained by comparison to table-top experiments.