Related papers: Second order front tracking algorithm for Stefan p…
We present a computational method for the simulation of the solidification of multicomponent alloys in the sharp-interface limit. Contrary to the case of binary alloys where a fixed point iteration is adequate, we hereby propose a…
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…
A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…
We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…
This paper considers a safe trajectory tracking of the Stefan problem with a second-order moving boundary dynamics. The model is given by a parabolic Partial Differential Equation (PDE) defined on a time-varying domain of moving boundary…
We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of two-phase, compressible, inviscid flow with a trivial mixture…
In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of…
Analysing data from Smoothed Particle Hydrodynamics (SPH) simulations is about understanding global fluid properties rather than individual fluid elements. Therefore, in order to properly understand the outcome of such simulations it is…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…
Purpose - This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach - A front-tracking/finite volume method introduced in Part I…
Modeling phase change problems numerically is vital for understanding many natural (e.g., ice formation, steam generation) and engineering processes (e.g., casting, welding, additive manufacturing). Almost all phase change materials (PCMs)…
The solidification behavior of liquid metal in a container under rapid cooling process is one of the major concerns to be analyzed. In order to analyze its fundamental behavior, a three- dimensional (3D) fluid dynamics simulation was…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…