mirror of
https://github.com/OPM/opm-simulators.git
synced 2025-01-11 00:41:56 -06:00
13 lines
1006 B
TeX
13 lines
1006 B
TeX
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
% This file has been autogenerated from the LaTeX part of the %
|
|
% doxygen documentation; DO NOT EDIT IT! Change the model's .hh %
|
|
% file instead!! %
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\-This model implements laminar \-Stokes flow of a single fluid, solving a momentum balance\-: \[ \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left(p_g {\bf {I}} - \mu_g \left(\boldsymbol{\nabla} \boldsymbol{v}_g + \boldsymbol{\nabla} \boldsymbol{v}_g^T\right)\right) - \varrho_g {\bf g} = 0, \]
|
|
|
|
and the mass balance equation\-: \[ \frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 \]
|
|
|
|
\-This is discretized by a fully-\/coupled vertex-\/centered finite volume (box) scheme in space and by the implicit \-Euler method in time.
|
|
|