In this study, a mathematical model is introduced to simulate the coupled heat transfer equation and Stefan condition occurring in moving boundary problems such as the solidification process in the continuous casting machines. In the continuous casting process, there exists a two-phase Stefan problem with moving boundary. The control-volume finite difference approach together with the boundary ...

The friction force on the moving interface between two different vacuum states of superfluid 3He is considered at low temperature. Since the dominating mechanism of the friction is the Andreev reflection of the massless " relativistic " fermions, which live on the A-phase side of the interface, the results are similar to that for the perfectly reflecting mirror moving in the quantum vacuum.

A new model is introduced for two-dimensional crystalline interfaces with negligible surface tension. The model is given by a discrete version of the linear molecular beam epitaxy (MBE) equation plus an additional term periodic in the interface height variable. Langevin dynamics simulations and analytical arguments show that the model exhibits a roughening transition to the high temperature pha...

We provide an overview of the finite element methods we developed in recent years for computation of fluid dynamics problems with moving boundaries and interfaces. This class of problems include those with free surfaces, two-fluid interfaces, fluid–object and fluid–structure interactions, and moving mechanical components. The methods developed can be classified into two main categories: interfa...