scholarly journals Reiterated Homogenization in $BV$ via Multiscale Convergence

2012 ◽  
Vol 44 (3) ◽  
pp. 2053-2098 ◽  
Author(s):  
Rita Ferreira ◽  
Irene Fonseca
Keyword(s):  
Multiscale Convergence ◽  
Reiterated Homogenization

scholarly journals Multiscale convergence and reiterated homogenization of parabolic problems

2005 ◽  
Vol 50 (2) ◽  
pp. 131-151 ◽  
Author(s):  
Anders Holmbom ◽  
Nils Svanstedt ◽  
Niklas Wellander
Keyword(s):  
Parabolic Problems ◽  
Multiscale Convergence ◽  
Reiterated Homogenization

scholarly journals FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2016 ◽  
Vol 15 (1) ◽  
pp. 96
Author(s):  
E. Iglesias-Rodríguez ◽  
M. E. Cruz ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
R. Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Small Parameter ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Small Scale ◽  
Multiple Spatial Scales ◽  
Effective Coefficients ◽  
Reiterated Homogenization

Heterogeneous media with multiple spatial scales are finding increased importance in engineering. An example might be a large scale, otherwise homogeneous medium filled with dispersed small-scale particles that form aggregate structures at an intermediate scale. The objective in this paper is to formulate the strong-form Fourier heat conduction equation for such media using the method of reiterated homogenization. The phases are assumed to have a perfect thermal contact at the interface. The ratio of two successive length scales of the medium is a constant small parameter ε. The method is an up-scaling procedure that writes the temperature field as an asymptotic multiple-scale expansion in powers of the small parameter ε . The technique leads to two pairs of local and homogenized equations, linked by effective coefficients. In this manner the medium behavior at the smallest scales is seen to affect the macroscale behavior, which is the main interest in engineering. To facilitate the physical understanding of the formulation, an analytical solution is obtained for the heat conduction equation in a functionally graded material (FGM). The approach presented here may serve as a basis for future efforts to numerically compute effective properties of heterogeneous media with multiple spatial scales.

FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2015 ◽  
Author(s):  
Ernesto Iglesias Rodríguez ◽  
Manuel Ernani Cruz ◽  
Julián Bravo-Castillero ◽  
Raúl Guinovart-Díaz ◽  
Reinaldo Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Multiple Spatial Scales ◽  
Reiterated Homogenization

REITERATED HOMOGENIZATION OF INTEGRAL FUNCTIONALS

2000 ◽  
Vol 10 (01) ◽  
pp. 47-71 ◽  
Author(s):  
ANDREA BRAIDES ◽  
DAG LUKKASSEN
Keyword(s):  
Energy Density ◽  
Quadratic Form ◽  
Phase Structure ◽  
Effective Properties ◽  
Effective Property ◽  
Integral Functionals ◽  
Effective Energy ◽  
Two Phase ◽  
Wide Range ◽  
Reiterated Homogenization

We consider the homogenization of sequences of integral functionals defined on media with several length-scales. Our general results connected to the corresponding homogenized functional are used to analyze new types of structures and to illustrate the wide range of effective properties achievable through reiteration. In particular, we consider a two-phase structure which is optimal when the integrand is a quadratic form and point out examples where the macroscopic behavior of this structure underlines an effective energy density which is lower than that of the best possible multirank laminate. We also present some results connected to a reiterated structure where the effective property is extremely sensitive of the growth of the integrand.

Reiterated homogenization of monotone parabolic problems

2007 ◽  
Vol 53 (2) ◽  
pp. 217-232 ◽  
Author(s):  
Liselott Flodén ◽  
Anders Holmbom ◽  
Marianne Olsson ◽  
Nils Svanstedt
Keyword(s):  
Parabolic Problems ◽  
Reiterated Homogenization

REITERATED HOMOGENIZATION APPLIED TO NANOFLUIDS WITH AN INTERFACIAL THERMAL RESISTANCE

2020 ◽  
Vol 18 (3) ◽  
pp. 361-384
Author(s):  
Ernesto Iglesias-Rodríguez ◽  
Julián Bravo-Castillero ◽  
Manuel Ernani C. Cruz ◽  
Leslie D. Pérez-Fernández ◽  
Federico J. Sabina
Keyword(s):  
Thermal Resistance ◽  
Interfacial Thermal Resistance ◽  
Reiterated Homogenization
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