Formatting

docs/source/FluidTimeDiscretization.rst

@@ -12,12 +12,9 @@ In the predictor
 
 #. Define :math:`U^{MAC}`, the face-centered (staggered) MAC velocity which is used for advection.
 
-#. Define an approximation to the new-time state,:math:`(\varepsilon_g \rho_g U)^* = (\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}^*) + \rho_g g )`
+#. Define an approximation to the new-time state,:math:`(\varepsilon_g \rho_g U)^{*} = (\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}^{*}) + \rho_g g )`
 
-#. Project :math:`U^*` by solving
+#. Project :math:`U^{*}` by solving
     :math:`\nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^*`
     then defining
          :math:(\varepsilon_g  U)^{**} = (\varepsilon_g  U)^{*} - \frac{\varepsilon_g}{\rho_g} \nabla \phi
@@ -26,12 +23,7 @@ In the predictor
 
 In the corrector
 
-#. Define an approximation to the new-time state,:math:`(\varepsilon_g \rho_g U)^{***} = (\varepsilon_g \rho_g U)^n +  
-                                                          \Delta t ( (-1/2) \nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g)^n 
-                                                                     -(1/2) \nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g)^{**} 
-                                                                    + \varepsilon_g \nabla {p_g}^{n+1/2,*} 
-                                                                    + (1/2) \nabla \cdot \tau^n + (1/2) \nabla \cdot \tau^{**}
-                                                                    + \sum_{part} \beta_p (V_p - {U_g}^{**}) + \rho_g g )`
+#. Define an approximation to the new-time state,:math:`(\varepsilon_g \rho_g U)^{***} = (\varepsilon_g \rho_g U)^n +  \Delta t ( (-1/2) \nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g)^n -(1/2) \nabla \cdot (\varepsilon_g \rho_g U^{MAC} U_g)^{**} + \varepsilon_g \nabla {p_g}^{n+1/2,*} + (1/2) \nabla \cdot \tau^n + (1/2) \nabla \cdot \tau^{**} + \sum_{part} \beta_p (V_p - {U_g}^{**}) + \rho_g g )`
 
 #. Project :math:`U^{***}` by solving
     :math:`\nabla \cdot \frac{\varepsilon_g}{\rho_g} \nabla \phi = \nabla \cdot (\varepsilon_g  U)^{***}`