Proračun podzemnog toka metodom konačnih zapremina

Abstract

U disertaciji su razmatrane numerićke metode za rešavanje problema podzemnog strujanja, transporta mase i energije u anizotropnoj i deo po deo neprekidnoj sredini. Ovakvi problemi sreću se u hidrologiji, naftnoj industriji, ekologiji i drugim oblastima. Podzemno strujanje u zasićenoj sredini opisano je linearnom parcijalnom diferencijalnom

jednačinom, dok je u nezasićenoj sredini opisano Ričardsovom nelinearnom parcijalnom diferencijalnom jednačinom. Transport mase i energije opisan je advektivno-difuznim jednačinama...

The thesis considers numerical methods for the computation of subsurface flow and transport of mass and energy in an anisotropic piecewise continuous medium. This kind of problems arises in hidrology, petroleum engineering, ecology and other fields. Subsurface flow in a saturated medium is described by a linear partial differential equation, while in an unsaturated medium it is described by the Richards nonlinear partial differential equation. Transport of mass and energy is described by advectiondiffusion equations. The thesis considers several finite volume methods for the discretization of diffusive and advective terms. An interpolation method for discretization of diffusion through discontinuous media is presented. This method is applicable to several nonlinear finite volume schemes. The presence of a well in the reservoir determines the subsurface flow to a large extent. Standard numerical methods produce a completely wrong flux and an inaccurate hydraulic head distribution in the well viscinity. Two methods for the well flux correction are introduced in this thesis. One of these methods gives second-order accuracy for the hydraulic head and first-order accuracy for the flux. Explicit and implicit time discretizations are presented. Preservation of the maximum and minimum principles in all considered schemes is analyzed. All considered schemes are tested using numerical examples that confirm teoretical results.