Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures.

Yohan Davit (1) , Michel Quintard (1)

1 IMFT - Institut de mécanique des fluides de Toulouse

This paper is a first of a series aiming at revisiting technical aspects of the volume averaging theory. Here, we discuss the choice of the spatial averaging operator for periodic and quasiperiodic structures. We show that spatial averaging must be defined in terms of a convolution and analyze the properties of a variety of kernels, with a particular focus on the smoothness of average fields, the ability to attenuate geometrical fluctuations, Taylor series expansions, averaging of periodic fields and resilience to perturbations of periodicity. We conclude with a set of recommendations regarding kernels to use in the volume averaging theory.

Mots clés: Upscaling; Volume averaging; Spatial averaging operator; Convolution Kernel

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

Yohan Davit, Michel Quintard. Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures.. Transport in Porous Media, 2017, 119 (3), pp.555-584. ⟨10.1007/s11242-017-0899-8⟩. ⟨hal-03514244⟩