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...

Abstract In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The treats the fluid–solid interaction problem monolithic way, where governing equations both sub-domains are solved on single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). unified implementation developed, these distinguished only terms me...

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...

The motivation underpinning this work is the need to understand bubble generation mechanisms due to interactions between free surface and turbulent boundary layers as commonly seen near ship walls. As a canonical problem, we consider a turbulent plane Couette flow with vertical parallel sidewalls and an air-water interface established by gravity in the vertical direction. Two-phase Couette flow...

We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing Immersed Boundary Methods; i.e. the proposed algorithms calculate and apply the force-density in the extended solid domain to...

Motivated by a problem in which a heteroclinic orbit represents a moving interface between ordered and disordered crystalline states, we consider a class of slow–fast Hamiltonian systems in which the slow manifold loses normal hyperbolicity due to a transcritical or pitchfork bifurcation as a slow variable changes. We show that under assumptions appropriate to the motivating problem, a singular...

for the Mini-Workshop “VMS and Stabilized FE” Stabilized Methods for Free-Surface Flow Simulations Marek Behr Chair for Computational Analysis of Technical Systems Center for Computational Engineering Science RWTH Aachen University Steinbachstr. 53B, 52074 Aachen, Germany [email protected] Free-surface flow simulations are an important design and analysis tool in many areas of engineerin...