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Zusammenfassung:
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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. |