Speaker
Description
We present a general framework for multicontinuum homogenization for the
heterogeneous porous media flows. Multicontinuum homogenization is conceptually derived from multiscale finite element methods, particularly, the Generalized Multiscale Finite Element
Method (GMsFEM) and the Constraint Energy Minimizing GMsFEM. The latter approaches are shown to have a first-order convergence independent of scales and contrast. Multicontinuum homogenization selects multiscale basis functions such that the degrees of freedom have spatial continuity, which is essential for formulating macroscopic equations.
Second, in multicontinuum approaches, we assume that multiscale basis functions can be localized using the ideas from CEM-GMsFEM, and we separate basis functions into average and gradient parts. The local cell problems are formulated as constraint cell problems for averages and gradients for each macroscopic degree of freedom. The input for these cell problems is the characteristic functions of the continua, which can be obtained from local eigenvalue problems, in general. The expansion of the solution is used in a variational formulation of microscale systems with appropriate test functions, depending on the
quantity of interest. This leads to macroscale (upscaled) equations. We present a general theory and discuss various aspects related to pore-scale multi-phase flows, gravity-driven unstable flows, poroelasticity, and reactive flows.
| Country | USA |
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