Volume 4, Issue 3
A Macro Projective Integration Method in 2D Microscopic System Applied to Nonlinear Ion Acoustic Waves in a Plasma

A. M. Maluckov, S. Ishiguro & M. M. Skoric

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Commun. Comput. Phys., 4 (2008), pp. 556-574.

Published online: 2008-09

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  • Abstract

IntheEquation-freeframework,amacro-coarseprojectiveintegrationmethod consists of two parts: the time stepper and time projection on macro scale. The first one consists of lifting, micro simulation and restriction. For extracting directly from microscopic simulations the information which would be obtained from the macroscopic model of two-dimensional microscopic systems, the time stepper based on the one-dimensional cumulative distribution functions, the marginal cumulative and appropriate number of the conditional cumulative distributions, is introduced. Here this procedure is tested on the nonlinear ion acoustic wave in a plasma. The numerical micro-solver is the one dimensional electrostatic particle-in-cell code. It is shown that particle 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 of correlations, trapping of particles during the wave steepening can seriously violate the basic assumptions of the equation-free approach.


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@Article{CiCP-4-556, author = {A. M. Maluckov, S. Ishiguro and M. M. Skoric}, title = {A Macro Projective Integration Method in 2D Microscopic System Applied to Nonlinear Ion Acoustic Waves in a Plasma}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {3}, pages = {556--574}, abstract = {

IntheEquation-freeframework,amacro-coarseprojectiveintegrationmethod consists of two parts: the time stepper and time projection on macro scale. The first one consists of lifting, micro simulation and restriction. For extracting directly from microscopic simulations the information which would be obtained from the macroscopic model of two-dimensional microscopic systems, the time stepper based on the one-dimensional cumulative distribution functions, the marginal cumulative and appropriate number of the conditional cumulative distributions, is introduced. Here this procedure is tested on the nonlinear ion acoustic wave in a plasma. The numerical micro-solver is the one dimensional electrostatic particle-in-cell code. It is shown that particle 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 of correlations, trapping of particles during the wave steepening can seriously violate the basic assumptions of the equation-free approach.


}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7804.html} }
TY - JOUR T1 - A Macro Projective Integration Method in 2D Microscopic System Applied to Nonlinear Ion Acoustic Waves in a Plasma AU - A. M. Maluckov, S. Ishiguro & M. M. Skoric JO - Communications in Computational Physics VL - 3 SP - 556 EP - 574 PY - 2008 DA - 2008/09 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7804.html KW - AB -

IntheEquation-freeframework,amacro-coarseprojectiveintegrationmethod consists of two parts: the time stepper and time projection on macro scale. The first one consists of lifting, micro simulation and restriction. For extracting directly from microscopic simulations the information which would be obtained from the macroscopic model of two-dimensional microscopic systems, the time stepper based on the one-dimensional cumulative distribution functions, the marginal cumulative and appropriate number of the conditional cumulative distributions, is introduced. Here this procedure is tested on the nonlinear ion acoustic wave in a plasma. The numerical micro-solver is the one dimensional electrostatic particle-in-cell code. It is shown that particle 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 of correlations, trapping of particles during the wave steepening can seriously violate the basic assumptions of the equation-free approach.


A. M. Maluckov, S. Ishiguro & M. M. Skoric. (1970). A Macro Projective Integration Method in 2D Microscopic System Applied to Nonlinear Ion Acoustic Waves in a Plasma. Communications in Computational Physics. 4 (3). 556-574. doi:
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