Defining and optimizing algorithms for neighbouring particle identification in SPH fluid simulations

Lagrangian particle methods such as smoothed particle hydrodynamics (SPH) are very demanding in terms of computing time for large domains. Since the numerical integration of the governing equations is only carried out for each particle on a restricted number of neighbouring ones located inside a cut-off radius rc, a substantial part of the computational burden depends on the actual search procedure; it is therefore vital that efficient methods are adopted for such a search. The cut-off radius is indeed much lower than the typical domain's size; hence, the number of neighbouring particles is only a little fraction of the total number. Straightforward determination of which particles are inside the interaction range requires the computation of all pair-wise distances, a procedure whose computational time would be unpractical or totally impossible for large problems. Two main strategies have been developed in the past in order to reduce the unnecessary computation of distances: the first based on dynamically storing each particle's neighbourhood list (Verlet list) and the second based on a framework of fixed cells. The paper presents the results of a numerical sensitivity study on the efficiency of the two procedures as a function of such parameters as the Verlet size and the cell dimensions. An insight is given into the relative computational burden; a discussion of the relative merits of the different approaches is also given and some suggestions are provided on the computational and data structure of the neighbourhood search part of SPH codes