Abstract: A coarse projective method for simulation of multi-dimensional macroscopic systems,Primal Equation Free Projective Integration(p-EFPI)method,was developed and applied to simulation of plasma ion acoustic wave.The method consists of two parts: Time stepper and time projection.For election velocities, probability distribution function or cumulative distrihution function are recorded in time to project,while,corresponding electron positions are reloaded(restricted)via electron charge density.Ion motion is assumed inherently coarse-grained as compared to electron dynamics,to describe possibly macro scale plasma evolution sufficiehtly well. To preserve full ion kinetic effects,individual ion orbits are tracked in time and simply extrapolate to pmject.This is one attempt to test method in p-EFPI framework on plasma physics phenomenon.Our calculations for ion acoustic wave paradigm indicate that P-EFPI simulation follows PIC results nice before ion trapping in phase space appears.However,as ion trapping takes place,main characteristic still keeps,except for ion trapping characteristic.

Key words: multi-scale simulations, p-FFPI, nonlinear plasmas, particle-in-cell(PIC)