Methods for computer-implemented simulation for the interaction of two or more objects are provided. Data describing particles that represent each of the objects is generated from geometric data for objects. The data for each particle describes a mass density, velocity and energy at a position of the corresponding object. The particles are grouped into sectors to define a computational mesh comprising a plurality of sectors, wherein each sector is a volume region at a position in space in which particles associated with the objects may reside. For each of a plurality of select particles, so called neighboring particles are determined that are within a region of influence with respect to a select particle. Computations are performed based on laws of conservation of mass, energy and momentum to produce updated values for mass, velocity, energy, pressure, stress and position for the particles at each of a plurality of time steps. According to one aspect, when determining neighboring particles for a given select particle, a search is made through a limited or bounded volume region with respect to the select particle that consists of the region of influence for the select particle at the previous time step and within those sectors in contact with or bordering the region of influence at the previous time step. According to another aspect, the plurality of select particles are identified as those particles that reside in an active sector, wherein an active sector is a sector that contains, or is adjacent to a sector that contains, particles that is actively involved in the engagement between the two objects. For example, an active sector is a sector that contains, or is adjacent to a sector that contains, at least one particle that has a velocity, pressure or stress greater than a corresponding predetermined amount.
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