mirror of
https://github.com/OPM/opm-simulators.git
synced 2024-12-23 16:00:01 -06:00
19 lines
1.6 KiB
TeX
19 lines
1.6 KiB
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 a non-\/isothermal two-\/component \-Stokes flow of a fluid solving a momentum balance, a mass balance, a conservation equation for one component, and one balance equation for the energy.
|
|
|
|
\-Momentum \-Balance\-: \[ \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left(p_g {\bf {I}} - \mu_g \left(\boldsymbol{\nabla} \boldsymbol{v}_g + \boldsymbol{\nabla} \boldsymbol{v}_g^T\right)\right) - \varrho_g {\bf g} = 0, \]
|
|
|
|
\-Mass balance equation\-: \[ \frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 \]
|
|
|
|
\hyperlink{a00047}{\-Component} mass balance equation\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \boldsymbol{\nabla} X_g^\kappa \right) - q_g^\kappa = 0 \]
|
|
|
|
\-Energy balance equation\-: \[ \frac{\partial (\varrho_g u_g)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \varrho_g h_g {\boldsymbol{v}}_g - \lambda_g \boldsymbol{\nabla} T - q_T = 0 \]
|
|
|
|
\-This is discretized using a fully-\/coupled vertex centered finite volume (box) scheme as spatial and the implicit \-Euler method as temporal discretization.
|
|
|