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17 lines
1.4 KiB
TeX
17 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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\-This model implements an isothermal two-\/component \-Stokes flow of a fluid solving a momentum balance, a mass balance and a conservation equation for one component.
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\-Momentum \-Balance\-: \[ \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left(p_g {\bf {I}} - \mu_g \left(\boldsymbol{\nabla} \boldsymbol{v}_g + \boldsymbol{\nabla} \boldsymbol{v}_g^T\right)\right) - \varrho_g {\bf g} = 0, \]
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\-Mass balance equation\-: \[ \frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 \]
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\hyperlink{a00047}{\-Component} mass balance equation\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \boldsymbol{\nabla} X_g^\kappa \right) - q_g^\kappa = 0 \]
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\-This is discretized using a fully-\/coupled vertex centered finite volume (box) scheme as spatial and the implicit \-Euler method as temporal discretization.
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