This paper presents a brief review of grand challenges of Smoothed Particle Hydrodynamics (SPH) method. As a meshless method, SPH can simulate a large range of applications from astrophysics to free-surface flows, to complex mixing problems in industry and has had notable successes. As a young computational method, the SPH method still requires development to address important elements which prevent more widespread use. This effort has been led by members of the SPH rEsearch and engineeRing International Community (SPHERIC) who have identified SPH Grand Challenges. The SPHERIC SPH Grand Challenges (GCs) have been grouped into 5 categories: (GC1) convergence, consistency and stability, (GC2) boundary conditions, (GC3) adaptivity, (GC4) coupling to other models, and (GC5) applicability to industry. The SPH Grand Challenges have been formulated to focus the attention and activities of researchers, developers, and users around the world. The status of each SPH Grand Challenge is presented in this paper with a discussion on the areas for future development.

Dynamic boundary conditions (DBC) for solid surfaces are standard in the weakly compressible smoothed particle hydrodynamics (SPH) code DualSPHysics. A stationary solid is simply represented by fixed particles with pressure from the equation of state. Boundaries are easy to set up and computations are relatively stable and efficient, providing robust numerical simulation for complex geometries. However, a small unphysical gap between the fluid and solid boundaries can form, decreasing the accuracy of pressures measured on the boundary. A method is presented where the density of solid particles is obtained from ghost positions within the fluid domain by linear extrapolation. With this approach, the gap between fluid and boundary is reduced and pressures in still water converge to hydrostatic, including the case of a bed with a sharp corner. The violent free-surface cases of a sloshing tank and dam break impact on an obstacle show pressures measured directly on solid surfaces in close agreement with experiments. The complex 3-D flow in a fish pass, with baffles to divert the flow, is simulated showing close agreement with measured water levels with weirs open and gates closed, but less close with gates open and weirs closed. This indicates the method is suitable for rapidly varying free-surface flows, but development for complex turbulent flows is necessary. The code with the modified dynamic boundary condition (mDBC) is available in DualSPHysics to run on CPUs or GPUs.