The past two decades have borne remarkable progress in our understanding of flow
mechanisms and numerical simulation approaches of shale gas reservoir, with much larger …

In this paper, we discuss a general multiscale model reduction framework based on
multiscale finite element methods. We give a brief overview of related multiscale methods …

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …

Complex processes in perforated domains occur in many real-world applications. These
problems are typically characterized by physical processes in domains with multiple scales …

Inherently coupled flow and geomechanics processes in fractured shale media have
implications for shale gas production. The system involves highly complex geo-textures …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

In this work, heat and mass transfer in a hypothetical Enhanced Geothermal System with
complex fracture network is considered. Fracture networks have complex geometries, exist …

In this paper, we develop a multiscale model reduction technique that describes shale gas
transport in fractured media. Due to the pore-scale heterogeneities and processes, we use …

Local multiscale methods often construct multiscale basis functions in the offline stage
without taking into account input parameters, such as source terms, boundary conditions …

In this contribution we present a survey of concepts in localized model order reduction
methods for parameterized partial differential equations. The key concept of localized model …