diff --git a/docs/source/FluidEquations.rst b/docs/source/FluidEquations.rst index 54faa623da8a69a2e9a85dca8ee43f82a9f7b405..892774f66fe4338768a3c19d8c4675231fea4dc6 100644 --- a/docs/source/FluidEquations.rst +++ b/docs/source/FluidEquations.rst @@ -3,12 +3,21 @@ Fluid Equations Below are the governing equations for the fluid: -.. math:: \frac{\partial (\epsilon_g \rho_g)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g) = 0 +Conservation of fluid mass: + +.. math:: \frac{\partial (\varepsilon_g \rho_g)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g) = 0 :label: eqn::mass_cons -.. math:: \frac{ \partial (\epsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g U_g) + \epsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g} +Conservation of fluid momentum: + +.. math:: \frac{ \partial (\varepsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g U_g) + \varepsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g} + + \sum_{part} \beta (V_{part} - U_g) :label: eqn::mom_cons -.. math:: \frac{\partial \epsilon_g}{\partial t} + \nabla \cdot (\epsilon_g U_g) = 0 - :label: eqn::mass_eps +Conservation of fluid volume: + +where $\sum_{part} \beta (V_{part} - U_g)$ is the drag term in which $V_{part}$ represents the particle velocity. + +.. math:: \frac{\partial \varepsilon_g}{\partial t} + \nabla \cdot (\varepsilon_g U_g) = 0 + :label: eqn::mass_vareps