A NUMERICAL SMOOTHED PARTICLES HYDRODYNAMICS METHOD IN 3-D FORMULATION FOR PHYSICAL PROCESS SIMULATION CONSIDERING THE COLLISION AND IMPACT PROBLEMS

V.V. Bashurov, A.V. Patyanina
VANT. Ser.: Mat. Mod. Fiz. Proc 1999. Вып.1. С. 26-38.

      A smoothed particles hydrodynamics method is based on 3-D free-Lagrangian algorithm not using a regular grid and regular grid functions. The continuum conservation laws written in the .form of differential relations are transformed into integral relations using interpolating function allowing to evaluate quantity field values in a point. As no space grid exists a space dif-ferentiation is carried from physical quantities to interpolating core, which represents an analytical function.
      The algorithm describes medium elements as material clouds smeared along the space which mass centres move according to conservation laws of continuum dynamics. Any physical quantity in any point of the space is evaluated by summing inserts from each particle into this point.
      A necessary stability condition was obtained for 3-D gas dynamics formulation using a spectral analysis method.
      The results of a given numerical method application are presented for physical process simulation.

      This work outlines a smoothed particles hydrodynamics method (SPH-method), a multithread parallelization principle for this algorithm in Windows NT operational environment and computed data for test problems in single- and multiprocessor variants.