TABLE OF CONTENTS In the SPH method, since the smoothing function has a compact support domain, only a finite number of particles are within the support domain of dimension ?h of the concerned particle, and are used in the particle approximations. These particles are generally referred to as nearest neighboring particles (NNP) for the concerned particle. The process of finding the near nearest particles is commonly referred to as nearest neighboring particle searching (NNPS). Unlike a grid-based numerical method, where the position of neighbor grid-cells are well defined once the grids are given, the nearest neighboring particles in the SPH for a given particle can vary with time. Three NNPS approaches, all-pair search, linked-list search algorithm, and tree search algorithm, are popular in SPH applications.
A direct and simple NNPS algorithm is the all-pair search approach (as shown in Figure 4.14). For a given particle i, the all-pair approach calculates the distance r ij from i to each and every particle j (=1, 2, , N), where N is the total number of particles in the problem domain. If the distance r ij is smaller than the dimension of the support domain for particle i, ?h, particle j is found belonging to the support domain of particle i. If the symmetric smoothing length is employed, particle i is also within the support domain of particle j. Therefore,...
