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