Physical Interpretations of the Numerical Instabilities in Diffusion Equations Via Statistical Thermodynamics

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Show simple item record BIGERELLE, maxence IOST, Alain 2015-07-17T13:20:12Z 2015-07-17T13:20:12Z 2004 2015-07-17T09:11:42Z
dc.description.abstract The aim of this paper is to analyze the physical meaning of the numerical instabilities of the parabolic partial differential equations when solved by finite differences. Even though the explicit scheme used to solve the equations is physically well posed, mathematical instabilities can occur as a consequence of the iteration errors if the discretisation space and the discretisation time satisfy the stability criterion. To analyze the physical meaning of these instabilities, the system is divided in sub-systems on which a Brownian motion takes place. The Brownian motion has on average some mathematical properties that can

be analytically solved using a simple diffusion equation. Thanks to this mesoscopic discretisation, we could prove that for each half sub-cell the equality stability criterion corresponds to an inversion of the particle flux and a decrease in the cell entropy in keeping with time as criterion increases. As a consequence, all stability criteria defined in literature can be used to define a physical continuous 'time-length' frontier on which mesoscopic and microscopic models join.
dc.language.iso en
dc.publisher Freund Publishing House Ltd.
dc.rights Post-print
dc.subject Diffusion en
dc.subject Partial Differential Equations en
dc.subject Finite Difference Method en
dc.subject Stability en
dc.subject fractal en
dc.subject Monte Carlo en
dc.title Physical Interpretations of the Numerical Instabilities in Diffusion Equations Via Statistical Thermodynamics en
dc.typdoc Articles dans des revues avec comité de lecture
dc.localisation Centre de Lille
dc.subject.hal Mathématique: Théorie de l'information et codage
ensam.audience Internationale 121-134
ensam.journal International Journal of Nonlinear Sciences and Numerical Simulation
ensam.volume 5
ensam.issue 2

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