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Portugaliae Mathematica

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Volume 70, Issue 4, 2013, pp. 319–344
DOI: 10.4171/PM/1937

Published online: 2013-12-31

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

Patrick Engel[1], Adrian Viorel[2] and Christian Rohde[3]

(1) Universität Stuttgart, Germany
(2) Babeş-Bolyai University, Cluj-Napoca, Romania
(3) Universität Stuttgart, Germany

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.

Keywords: Phase Transition in Elastic Bars, Viscosity-Capillarity Regularization, Asymptotics, Numerical Approximations

Engel Patrick, Viorel Adrian, Rohde Christian: A low-order approximation for viscous-capillary phase transition dynamics. Port. Math. 70 (2013), 319-344. doi: 10.4171/PM/1937