Simulation method and simulation apparatus

摘要

To obtain velocity, density, pressure, and a position per unit time, acceleration of each particle and a repulsive force applied to each particle from a boundary surface is obtained by an equation of motion discretized by a predetermined kernel function; velocity after unit time is calculated by time integration; a density time differential is calculated by a discretized continuity equation representing a temporal change in the density based on a predetermined kernel function; density after unit time is calculated by time integration on the density time differential by using the velocity after the unit time; smoothing is performed on the density at predetermined intervals; pressure after unit time is calculated by an equation of state with the density after unit time; a position after unit time is calculated; the above calculations are repeated from the initial state to the end of a predetermined time.

主权项

1. A simulation method of analyzing a state of each of particles that comprise a set that represents a continuum, the simulation method comprising:
calculating, using a processor, acceleration of each of the particles and a repulsive force applied to each of the particles from a boundary surface, by using an equation of motion that is discretized by a kernel function representing a degree of contribution of one of the particles to influence on the other particles, based on input initial values of velocity, density, pressure, and a position of each of the particles; calculating, using a processor, velocity of each of the particles after a unit time based on a current position of each of the particles by performing time integration on current velocity at the current position of each of the particles based on the calculated acceleration and the calculated repulsive force; calculating a density time differential of each of the particles by using a continuity equation that is discretized by the kernel function so as to represent a temporal change in the density of the continuum; calculating, using the processor, density of each of the particles after the unit time by performing time integration on the calculated density time differential of each of the particle by using the velocity of each of the particles after the unit time based on the current position of each of the particles; performing smoothing on the density of each of the particles after the unit time, once every predetermined number of calculations of the density of each of the particles; calculating, using the processor, pressure of each of the particles after the unit time by using an equation of state based on the density of each of the particles after the unit time; calculating, using the processor, a position of each of the particles after the unit time by performing time integration based on the velocity of each of the particles after the unit time based on the current position of each of the particles; and acquiring velocity, density, pressure, and a position of each of the particles per unit time by repeating the calculations of the velocity, the density, the pressure, and the position of each of the particles from the initial state till an end of a predetermined time; wherein the acceleration is represented byⅆvaⅆt=⁢-∑b⁢⁢mb⁡(pb+paρb⁢ρa)⁢∇a⁢Wab⁢-∑b⁢⁢mb⁡(βav⁢ϕ2ρab)⁢∇a⁢Wab,⁢+g⁢ where a subscript a indicates information on a particle a, where a subscript b indicates information on a particle b, where the particle a is a particle that is arbitrarily extracted from the particles, where the particle b is a neighboring particle of the particle a, where ρa is a density of the particle a, where ρb is a density of the particle b, where ρab represents an arithmetic average of ρa and ρb, where pa is a pressure applied to the particle a, where pb is a pressure applied to the particle b, where Wab is a kernel function with the particle a and the particle b where ∇a represents a vector differential operator at the position of the particle a, where mb is a mass of the particle b, and where a term g represents an external force term.