Skip to content
Snippets Groups Projects
Commit 1577eeb5 authored by Ann Almgren's avatar Ann Almgren
Browse files

formatting

parent 9f2f1662
No related branches found
No related tags found
No related merge requests found
......@@ -14,23 +14,22 @@ In the predictor
#. Define an approximation to the new-time state, :math:`(\varepsilon_g \rho_g U)^{\ast}` by setting
.. math::(\varepsilon_g \rho_g U)^{\ast} = (\varepsilon_g \rho_g U)^n +
\Delta t ( -\nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g) + \varepsilon_g \nabla {p_g}^{n-1/2} +
\nabla \cdot \tau^n + \sum_{part} \beta_p (V_p - {U_g}^{\ast}) + \rho_g g )
.. math:: (\varepsilon_g \rho_g U)^{\ast} = (\varepsilon_g \rho_g U)^n +
\Delta t ( -\nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g) + \varepsilon_g \nabla {p_g}^{n-1/2} +
\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}`
then defining
.. 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
and
and
.. 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
......@@ -41,14 +40,14 @@ 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
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
and
.. math:: {p_g}^{n+1/2} = {p_g}^{n-1/2} + \phi
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment