%BND_free%
hydrostatic pressure free surface boundary condition
Hydrostatic pressure free surface boundary condition with given ambient pressure
Syntax:
Equation:
The pressure at the free surface is given by the dynamic, viscous stretch of the free surface. The general condition is
\begin{align} p_\text{hyd} + p_\text{dyn} = p^{outer}_\text{dyn} + p^{outer}_\text{hyd} + p_{\sigma} + {\bf n}^T ( {\bf S}_\text{v} + {\bf S}_s ) {\bf n}\end{align}
where
\begin{align} p_\sigma = \sigma \kappa\end{align}
The hydrostatic part of the free surface condition for pressure is given by (
OuterHydrostaticPressure = \( p^{outer}_\text{hyd}\))
\begin{align} p_\text{hyd} = p^{outer}_\text{hyd} + p_\sigma + {\bf n}^T\cdot {\bf S}_s \cdot n\end{align}
Notation:
-
- \( p^{outer}_\text{hyd}\): ambient/outer hydrostatic pressure
- \( p_\sigma\): pressure difference due to surface tension
- \( \sigma\): surface tension (see sigma, %ind_SIG%)
- \( \kappa\): curvature of the free surface (see %ind_kappa%)