Graduate Thesis Or Dissertation
 

Multiscale analysis of saturated flow in a porous medium with an adjacent thin channel

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/pc289n42r

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  • This thesis contains three parts addressing the asymptotic analysis of fluid flow through fully saturated porous medium in the presence of an adjacent thin channel. In the first part the problem is modeled by Darcy's law in both the porous medium and in the channel. The permeability in the channel is scaled in order to balance the width of the channel with the high permeability in this region. The geometry of the channel is a region between a flat interface with the porous medium and a curvy top. The problem is analyzed in direct variational formulation, and the solution obeys the minimization principle. A fully-coupled model with a lower dimensional interface problem is obtained in the limit as an approximation. The second part models the problem by means of the same Darcy's law and scaling technique. The difference consists of the geometric possibilities of the channel, which is now limited by two parallel surfaces of smoothness C¹, and the formulation of the problem as a saddle point solution of a system of first order partial differential equations in mixed formulation. A limit problem of analogous structure and lower dimensional interface is obtained as an approximation. In the third part the channel is modeled with Stokes law. Appropriate interface conditions are given to couple the Stokes' and Darcy's flow. The tangential velocity and the pressure exhibit a discontinuity across the interface. The limit problem is a Darcy-Brinkman system which has a structure different from that of the original one.
  • Keywords: Darcy, Modeling, Homogenization, Porous Media, Partial Differential Equations, Stokes
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