opm-simulators/doc/handbook/ModelDescriptions/1pdecoupledmodel.tex
Andreas Lauser 7deaf50402 box model descriptions: syncronize them with the doxygen versions
the descriptions of the semi-implicit models are imported from dumux
because I suppose that these have been modified manually and the
differences should be negligible anyway...
2012-10-19 13:49:54 +02:00

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This model solves equations of the form \[ \textbf{div}\, \boldsymbol v = q. \] The velocity $ \boldsymbol v $ is the single phase Darcy velocity\-: \[ \boldsymbol v = -\frac{1}{\mu} \boldsymbol K \left(\textbf{grad}\, p + \rho \, g \, \textbf{grad}\, z\right), \] where $ p $ is the pressure, $ \boldsymbol K $ the absolute permeability, $ \mu $ the viscosity, $ \rho $ the density, and $ g $ the gravity constant, and $ q $ is the source term. At the boundary, $ p = p_D $ on $ \Gamma_{Dirichlet} $, and $ \boldsymbol v \cdot \boldsymbol n = q_N$ on $ \Gamma_{Neumann} $.