Related papers: Accretion and Ablation in Deformable Solids using …
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example,…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…
Experimental results on amorphous ZrAlCu thin film growth and the dynamics of the surface morphology as predicted from a minimal nonlinear stochastic deposition equation are analysed and compared. Key points of this study are (i) an…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
We present a numerical method specifically designed for simulating three-dimensional fluid--structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids…
A problem of mass flow in the immediate vicinity of a planet embedded in a protoplanetary disk is studied numerically in two dimensions. Large differences in temporal and spatial scales involved suggest that a specialized discretization…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…
We develop and evaluate a numerical procedure for a system of nonlinear differential equations, which describe the propagation of solitons into ideal dielectric optical fibers. This problem has analytical solutions known. The numerical…
We investigate novel fitted finite element approximations for two-phase Navier--Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian--Eulerian (ALE) finite element formulations. The moving interface is approximated…
A numerical method is presented to simulate gas-liquid-solid flows with bubble-particle interaction, including particle collision, sliding, and attachment. Gas-liquid flows are simulated in an Eulerian framework using a volume-of-fluid…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…