Adaptive Smoothed Particle Hydrodynamics Neighbor Search Algorithm for Large Plastic Deformation Computational Solid Mechanics

Smoothed Particle Hydrodynamics (SPH) has quickly become one of the most popular mesh-free methods since its introduction in 1977. In the recent years, a great amount of research has been focused on addressing some of the common computational time associated with the SPH method. One of the remaining hurdles is the long computational associated with building the neighbor list. Because of the nature of the original SPH codes (astropyshics), the neighbor search is commonly performed for every element in the domain at each time step. In this work, we develop an optimized neighbor search algorithm that is suitable for deployment on NVidia graphics cards (GPU). The SPH code is written using CUDA Fortran. The algorithm can be used for large plastic deformation computational solid mechanics (CSM) problems. The search uses an adaptive algorithm that updates the neighbor list for individual SPH elements depending whether a plastic strain increment threshold is surpassed. The neighbor list as well as the inter-particle spacing (r ij) is re-used for elements that do not surpass the search update criteria. Although in this work we use a Cell based search, the algorithm can be easily adapted for the Direct Search, the Verlet List or a Tree Sort approach. Monaghan's artificial stress term is added to the momentum equation to suppress the common tensile instability. The XSPH approach is used to update the positions of the SPH elements. The algorithm is shown to reduce the overall computation time by up to 70% without loss of accuracy for CSM simulations when compared with the non-adaptive search method.