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Patch dynamics: macroscopic simulation of multiscale systems
Author(s) -
Samaey Giovanni,
Kevrekidis Ioannis G.,
Roose Dirk
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700767
Subject(s) - partial differential equation , finite volume method , mathematics , scheme (mathematics) , finite difference , derivative (finance) , partial derivative , statistical physics , computer science , physics , mathematical analysis , mechanics , financial economics , economics
We describe a numerical algorithm to perform time integration of a partial differential equation (PDE) which is not available in closed from; instead we are given a more microscopic description of the system behaviour. The proposed methods mimic a macroscopic finite difference (FD) or finite volume (FV) scheme for the unavailable PDE; they extract a macroscopic time derivative (for FD schemes) or flux (for FV schemes) from appropriately initialized, but otherwise unconstrained simulations with the given microscopic model. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)