A Macro Projective Integration Method in 2D Microscopic System Applied to Nonlinear Ion Acoustic Waves in a Plasma (Communications in Computational Physics, 2008)
In the Equation-free framework, a macro-coarse projective integration methodconsists of two parts: the time stepper and time projection on macro scale. The firstone consists of lifting, micro simulation and restriction. For extracting directly frommicroscopic simulations the information which would be obtained from the macroscopic model of two-dimensional microscopic systems, the time stepper based on theone-dimensional cumulative distribution functions, the marginal cumulative and appropriate number of the conditional cumulative distributions, is introduced. Here thisprocedure is tested on the nonlinear ion acoustic wave in a plasma. The numericalmicro-solver is the one dimensional electrostatic particle-in-cell code. It is shown thatparticle correlations related to wave structures are better preserved by the new model.The lifting step is critically related to the noise in system. The enlarged noise, rise ofcorrelations, trapping of particles during the wave steepening can seriously violate thebasic assumptions of the equation-free approach.