FINITE ELEMENT METHOD FOR THE STOKES–DARCY PROBLEM WITH A BOUNDARY CONDITIONS

Author (s) : V.Silambarasan, A.Ramya ,B.Kavitha, D.Vidhya

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Abstract :
This paper considers numerical methods for approximating and simulating the Stokes– Darcy problem, with  boundary condition. We study a robust stabilized fully mixed discretization technique. This method ensures stability of the finite element scheme and does not use any Lagrange multipliers to introduce a stabilization term in the temporal Stokes–Darcy problem discretization. A correct finite element scheme is obtained and its convergence analysis is done. Finally, the efficiency and accuracy of these numerical methods are illustrated by different numerical tests. In this article, we focus on the study of fluid flow in different domains and different physical situations, for example, coupling of groundwater and surface flows, which are coupling of both surface and subsurface flows. This model is described with the Stokes–Darcy equation. This relationship is provided by the Stokes–Darcy linear equations with a contact interface. The Beavers and Joseph interface conditions in the Stokes–Darcy model, which have become a most important topic in research, can be found. Saffman modified this interface condition. This model arises in the hydrology, particularly, in groundwater flows, and in modeling of reservoirs in petroleum engineering. It is also used for describing many natural and industrial phenomena in biomedicine and industrial processes.

Keywords : Stokes–Darcy problem, mixed finite element method, free flow, porous media flow, stabilized scheme

Conference Date : 30/08/2019

Pages : 225

Paper ID : 19216