Numerical simulation of the transport and flow problems in perforated domains using generalized multiscale finite element method
V. N. Alekseev, U. Gavrileva, Спиридонов Денис Алексеевич, Aleksei Tyrylgin, Maria Vasilyeva · AIP conference proceedings · 2018
In this work, we consider flow and transport processes in perforated domains. Such processes have multiscale nature and occur in many real world applications, for example, in simulation of the carbonate reservoirs. The transport process is described by the convection-diffusion equation. The convection term in the transport equation is governed by a flow velocity field. The flow is described by Darcy equation. Numerical solutions for flow and transport equations in perforated domains are expensive and require resolving fine-scale details (perforations). For this reason, some type of model reduction is necessary. For coarse grid approximation, we use Generalized Multiscale Finite Element method (GMsFEM) for flow problem and construct local multiscale basis functions. We present numerical results for model problem in two-dimensional perforated domains.