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18 lines
1.4 KiB
TeX
18 lines
1.4 KiB
TeX
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% This file has been autogenerated from the LaTeX part of the %
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% doxygen documentation; DO NOT EDIT IT! Change the model's .hh %
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% file instead!! %
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Adaption of the BOX scheme to the one-\/phase two-\/component flow model. This model implements an one-\/phase flow of an incompressible fluid, that consists of two components, using a standard Darcy approach as the equation for the conservation of momentum: \[ v_{D} = - \frac{K}{\mu} \left(\text{grad} p - \varrho g \right) \]
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Gravity can be enabled or disabled via the Property system. By inserting this into the continuity equation, one gets \[ - \text{div} \left\{ \varrho \frac{K}{\mu} \left(\text{grad} p - \varrho g \right) \right\} = q \;, \]
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The transport of the components is described by the following equation: \[ \Phi \varrho \frac{ \partial x}{\partial t} - \text{div} \left( \varrho \frac{K x}{\mu} \left( \text{grad} p - \varrho g \right) + \varrho \tau \Phi D \text{grad} x \right) = q. \]
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All equations are discretized using a fully-\/coupled vertex centered finite volume (box) scheme as spatial and the implicit Euler method as time discretization.
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The primary variables are the pressure $p$ and the mole fraction of dissolved component $x$.
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