Commit 1577eeb5 authored by Ann Almgren's avatar Ann Almgren
Browse files

formatting

parent 9f2f1662

docs/source/FluidTimeDiscretization.rst

+6 −7
Original line number Diff line number Diff line
@@ -19,7 +19,9 @@ In the predictor 
           \nabla \cdot \tau^n + \sum_{part} \beta_p (V_p - {U_g}^{\ast}) + \rho_g g )



#. Project :math:`U^{\ast}` by solving

    :math:`\nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^{\ast}`



.. math:: \nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^{\ast}



then defining



.. math:: (\varepsilon_g  U)^{n+1} = (\varepsilon_g  U)^{***} - \frac{\varepsilon_g}{\rho_g} \nabla \phi
@@ -28,9 +30,6 @@ In the predictor 


.. math:: {p_g}^{n+1/2, \ast} = {p_g}^{n-1/2} + \phi



         :math:(\varepsilon_g  U)^{\ast \ast} = (\varepsilon_g  U)^{\ast} - \frac{\varepsilon_g}{\rho_g} \nabla \phi

    and 

         :math:`{p_g}^{n+1/2,\ast} = {p_g}^{n-1/2} + \phi`  



In the corrector
@@ -41,13 +40,13 @@ In the corrector 
          + \varepsilon_g \nabla {p_g}^{n+1/2,\ast} + (1/2) \nabla \cdot \tau^n + (1/2) \nabla \cdot \tau^{\ast \ast} + 

            \sum_{part} \beta_p (V_p - {U_g}^{\ast \ast}) + \rho_g g )



#. Project :math:`U^{***}` by solving

#. Project :math:`U^{\ast \ast \ast}` by solving



.. math:: \nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^{***}

.. math:: \nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^{\ast \ast \ast}



then defining



.. math:: (\varepsilon_g  U)^{n+1} = (\varepsilon_g  U)^{***} - \frac{\varepsilon_g}{\rho_g} \nabla \phi

.. math:: (\varepsilon_g  U)^{n+1} = (\varepsilon_g  U)^{\ast \ast \ast} - \frac{\varepsilon_g}{\rho_g} \nabla \phi



and