• Adaptive Multiscale Methods Based on A Posteriori Error Estimates 

      Alyaev, Sergey (Master thesis, 2010-06-01)
      We give an overview of different methods for solving highly heterogeneous elliptic problems with multiscale structure and no intuitive scale separation. We compare different finite element variational multiscale methods ...
    • Analysis of Control Volume Heterogeneous Multiscale Methods for Single Phase Flow in Porous Media 

      Alyaev, Sergey; Keilegarden, Eirik; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2014)
      The standard approximation for the flow-pressure relationship in porous media is Darcy's law that was originally derived for infiltration of water in fine homogeneous sands. Ever since there have been numerous attempts to ...
    • Fractal structures in freezing brine 

      Alyaev, Sergey; Keilegavlen, Eirik; Nordbotten, Jan Martin; Pop, Iuliu Sorin (Peer reviewed; Journal article, 2017-09)
      The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary ...
    • Multiscale analysis of selected problems in fluid dynamics 

      Alyaev, Sergey (Doctoral thesis, 2017-02-03)
      The world around us is inherently multiscale. The variety of different models depending on the reference scale is particularly diverse in problems of fluid-solid systems. For those systems, the geometry, effective parameters ...
    • Multiscale Simulation of Non-Darcy Flows 

      Alyaev, Sergey; Keilegarden, Eirik; Nordbotten, Jan Martin (Conference object; Peer reviewed, 2012-06)
      In this work we present control volume multiscale methods which address problems on the interaction between pore scale and Darcy scale. For the case when linear equations govern the ow on the pore scale our solution converges ...