The momentum transport equation is as follows:

\[\frac{\partial \rho \u}{\partial t} + \div (\u \u) + f_{MRF}(\rho, \u) + \div \vec{R} = - \grad p_{rgh} - (\vec{g} \cdot \vec{h} - (\vec{gh})_{\ref}) \grad \rho + \vec{S}_{\rho, \u}\]

where:

Property Description
\(t\) Time
\(\rho\) Density
\(\u\) Velocity
\(f_{MRF}\) Multiple reference frame function
\(\vec{R}\) Stress tensor
\(p_{rgh}\) Pressure excluding the hydrostatic contribution
\(\vec{h}\) Spatial coordinates
\(\vec{g}\) Gravitational acceleration
\(\vec{gh}_{ref}\) Reference hydrostatic pressure
\(\vec{S}\) Source term through fvOption

The pressure-term transformation involving the hydrostatic contribution is explained as follows: