Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

Yohan Davit (1) , Christopher G. Bell (2) , Helen Byrne (2) , Lloyd A. C. Chapman (2) , Laura S. Kimpton (2) , Georgina E. Lang (2) , Katherine H. L. Leonard (2) , James M. Oliver (2) , Natalie C. Pearson (2) , Rebecca J. Shipley (3) , Sarah L. Waters (2) , Jonathan P. Whiteley (2) , Brian D. Wood (4) , Michel Quintard (1)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 University of Oxford
3 UCL - University College of London [London]
4 OSU - Oregon State University

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works.

Mots clés: Homogenization; Volume averaging; Multiscale asymptotics; Upscaling; Porous media

Domaines: Mécanique des fluides [physics.class-ph]

Yohan Davit, Christopher G. Bell, Helen Byrne, Lloyd A. C. Chapman, Laura S. Kimpton, et al.. Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?. Advances in Water Resources, 2013, 62 (part B), pp.178-206. ⟨10.1016/j.advwatres.2013.09.006⟩. ⟨hal-03523136⟩