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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2016016637
pages 135-148

A SYSTEMATIC FORMULATION OF MULTIPHYSICS SYSTEMS AND ITS APPLICATIONS TO BOUNDARY LAYERS AND SHOCK PROFILES

Ismael Herrera Revilla
Modelacion Matematica y Computacional, Departamento de Recursos Naturales, Instituto de Geofisica, Universidad Nacional Autonoma de Mexico, Apdo. Postal 22-220, Mexico, D.F. 14000
http://www.mmc.geofisica.unam.mx/iherrera/

ABSTRACT

There are two approaches to multiscale modeling: information passing and concurrent, and the latter one is further divided into overlapping and non-overlapping. This paper presents a general and systematic method for treating concurrent non-overlapping approaches to multiscale modeling that can be applied whenever both the coarse and fine resolutions belong to the realm of continuum mechanics. These results are derived from an axiomatic formulation of the mathematical models of continuum mechanics previously introduced by the author. Applications of such a method tolocal events yield a bi-physical approach to them, which in turn permits deriving a new procedure for treating boundarylayers and shock profiles associated with singular perturbations of partial differential equations. Some advantages of the new procedure over standard methods are indicated in the paper.


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