Заседание семинара "Численный анализ" 19.12.2017 в 11-00. "Generalized multiscale methods for porous media flows and their applications.", Эфендиев Я.

Subsurface formations often display high degrees of variability over multiple length scales. This permeability's spatial variations and complex connectivity impact flow and transport. For this reason, these effects must be included in simulations of flows. Upscaling techniques are introduced to coarsen these geological models for flow calculations. The main idea of upscaling techniques is to formulate macroscopic equations on a coarse grid and ways to compute macroscopic parameters.It is important that these coarsened flow models replicate the fine scale characterizations. Recently, multiscale methods are introduced to perform coarse-grid simulations. In this talk,  I will give an overview of some multiscale methods and discuss their relation to flow-based upscaling. I will mostly focus on single-phase flow and show how to derive upscaled models and compute effective properties using multiscale methods and flow-based upscaling. I will describe subgrid errors in these methods and show a relation between multiscale methods and flow-based upscaling methods. Then, I will describe a general multiscale framework and show how one can achieve an accurate coarse-grid models using multi-continuum and non-local upscaling. I will describe some applications of multiscale methods to Bayesian approaches and inverse problems.