Momentum transport equation

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:

• Hydrostatic pressure effects