Proposal for fast calculation of particle interactions in SPH simulations

• A simple algorithm is presented for a fast calculation of kernel functions in SPH.
• The proposed technique will reduce significantly execution time of SPH simulations.
• Effectiveness of the proposed technique increases with the number of particles used.
• An explicit and handy formulation is proposed for practical usage.

A simple and easy algorithm is presented for a fast calculation of kernel functions which are required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. The present proposed algorithm improves the Linked-list algorithm and adopts the Pairwise interaction technique, both of which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The proposed algorithm is easy to implement without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, ratios between the sub-domain size and smoothing length and total amount of particles are conducted to determine the range of applicability and effectiveness of the proposed technique. A handy formulation which relates the ratio between the sub-domain size and smoothing length and the total amount of particles used in the simulation using the SPH method is proposed for practical usage.