Free surfaces modelling based on level sets

We use a finite element formulation of the level set method to model the evolution of the free surface of axi-symmetric spreading flows of highly viscous media on a horizontal plane. We consider specifically the growth of a lava dome as an example however similar problems also occur in flows involving the spreading of molten metals or ceramics. Here we restrict ourselves on constant viscosity fluids for simplicity. In real lavas or melts the viscosity is highly temperature dependent. This manifests itself in the formation of thin predominantly elastic-plastic boundary layers along the free (cold) surfaces of the spreading flows. In our model we follow Iverson [23] who assumes that the thin boundary layer behaves like an ideal plastic membrane shell enclosing the free surface. The effect of the membrane shell is then formally identical to a surface tension-like boundary condition for the normal stress at the free surface