A Multiphysics Framework to Learn and Predict in Presence of Multiple Scales

Abstract:

Modeling complex phenomena in the subsurface remains challenging due to the presence of multiple interacting scales, which can make it impossible to focus on purely macroscopic phenomena (relevant in most applications) and neglect the processes at the micro-scale. We present and discuss a general framework that allows us to deal with the situation in which the lack of scale separation requires the combined use of different descriptions at different scale (for instance, a pore-scale description at the micro-scale and a Darcy-like description at the macro-scale) [1,2].

The method is based on conservation principles and constructs the macro-scale problem by numerical averaging of micro-scale balance equations. By employing spatiotemporal adaptive strategies, this approach can efficiently solve large-scale problems [2,3]. In addition, being based on a numerical volume-averaging paradigm, it offers a tool to illuminate how macroscopic equations emerge from microscopic processes, to better understand the meaning of microscopic quantities, and to investigate the validity of the assumptions routinely used to construct the macro-scale problems.

[1] Tomin, P., and I. Lunati, A Hybrid Multiscale Method for Two-Phase Flow in Porous Media, Journal of Computational Physics, 250, 293–307, 2013

[2] Tomin, P., and I. Lunati, Local-global splitting and spatiotemporal-adaptive Multiscale Finite Volume Method, Journal of Computational Physics, 280, 214–231, 2015

[3] Tomin, P., and I. Lunati, Spatiotemporal adaptive multiphysics simulations of drainage-imbibition cycles, Computational Geosciences, 2015 (under review)