Flow and transport in perforated and fractured domains with Robin boundary conditions

  • Gavrilieva Uygulaana S., lanasemna@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677891, Russia
  • Alekseev Valentin N., alekseev.valen@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677891, Russia
  • Vasilyeva Maria V., vasilyevadotmdotv@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: transport equation, Stokes problem, perforated domain, fractured domain, numerical modeling, Robin boundary condition, numerical stabilization, SUPG, finite element method

Abstract

We consider transport and flow problems in perforated and fractured domains. The system of equations is described by the Stokes equation for modeling fluid flow and the equation for the concentration transfer of a certain substance. Concentration is supplemented by inhomogeneous boundary conditions of the third type which simulate the occurring reaction on the faces of the modeled object. For the numerical solution of the problem, a finite-element approximation of the equation is constructed. To obtain a sustainable solution to the transport problem, the SUPG (streamline upwind Petrov–Galerkin) method is used to stabilize the classical Galerkin method. The computational implementation is based on the Fenics computational library. The results of solving the model problem in perforated and fractured domains are presented. Numerical studies of various regimes of heterogeneous boundary conditions were carried out.

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How to Cite
Gavrilieva, U., Alekseev, V. and Vasilyeva, M. ( ) “Flow and transport in perforated and fractured domains with Robin boundary conditions”, Mathematical notes of NEFU, 24(3), pp. 65-77. doi: https://doi.org/10.25587/SVFU.2018.3.10890.
Section
Mathematical Modeling