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- there are no LaTeX files with capital letters anymore - there are no more "dangling" references
13 lines
1.9 KiB
TeX
13 lines
1.9 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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Provides a Finite Volume implementation for the pressure equation of a compressible system with two components. An I\-M\-P\-E\-S-\/like method is used for the sequential solution of the problem. Diffusion is neglected, capillarity can be regarded. Isothermal conditions and local thermodynamic equilibrium are assumed. Gravity is included. \[ c_{total}\frac{\partial p}{\partial t} + \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{\alpha} \bf{v}_{\alpha}\right) = \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} q^{\kappa}, \] where $\bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) $. $ c_{total} $ represents the total compressibility, for constant porosity this yields $ - \frac{\partial V_{total}}{\partial p_{\alpha}} $, $p_{\alpha} $ denotes the phase pressure, $ \bf{K} $ the absolute permeability, $ \lambda_{\alpha} $ the phase mobility, $ \rho_{\alpha} $ the phase density and $ \bf{g} $ the gravity constant and $ C^{\kappa} $ the total \hyperlink{a00070}{Component} concentration. See paper S\-P\-E 99619 or \char`\"{}\-Analysis of a Compositional Model for Fluid
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Flow in Porous Media\char`\"{} by Chen, Qin and Ewing for derivation.
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The pressure base class \hyperlink{a00131}{F\-V\-Pressure} assembles the matrix and right-\/hand-\/side vector and solves for the pressure vector, whereas this class provides the actual entries for the matrix and R\-H\-S vector. The partial derivatives of the actual fluid volume $ v_{total} $ are gained by using a secant method.
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