A low-order approximation for viscous-capillary phase transition dynamics

The dynamics of an elastic bar that appears in two phases can be described by viscosity-capillarity models. They contain numerically complicated third-order or fully nonlocal terms to account for surface energies. Based on work of Solci and Vitali [20] we analyze an alternative modelling approach that does not involve third-order differential operators. It is proven that solutions of the new model tend to solutions of the classical viscosity-capillarity model provided a so-called coupling parameter tends to infinity. Numerical experiments illustrate our findings. In fact it is shown that the new model provides a reliable and efficient approach to compute approximate solutions for the classical viscosity-capillarity model.