Free surface calculations

Free surface calculations#

In reality the boundary conditions of a convecting Earth are not no-slip or free slip (i.e., no normal velocity). Instead, we expect that a free surface is a more realistic approximation, since air and water should not prevent the flow of rock upward or downward. This means that we require zero stress on the boundary, or \(\sigma \cdot \textbf{n} = 0\), where \(\sigma = 2 \eta \varepsilon (\textbf{u})\). In general there will be flow across the boundary with this boundary condition. To conserve mass we must then advect the boundary of the domain in the direction of fluid flow. Thus, using a free surface necessitates that the mesh be dynamically deformable.