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An ALE FEM for solid-liquid phase transitions with free melt surface
TLDR
In this article, a finite element method is introduced which is capable of simulating the melting of solid material with a free melt surface, especially in a micro scale situation, the free capillary surface and its interplay with the solid-liquid interface play an important role.Abstract:
A finite element method is introduced which is capable to simulate the melting of solid material with a free melt surface. Especially in a micro scale situation, the free capillary surface and its interplay with the solid-liquid interface play an important role. The method is applied to the engineering process of melting the tip of a thin steel wire by laser heating. The mathematical system comprises heat conduction, radiative boundary conditions, and solid-liquid phase transition as well as the fluid dynamics in the liquid region and a free capillary surface. A sharp interface mesh–moving method (complemented by occasional remeshing) is used to track the liquid/solid interface as well as the capillary free boundary.read more
Citations
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3D Finite element simulation of a material accumulation process including phase transitions and a capillary surface
Mischa Jahn,Alfred Schmidt +1 more
TL;DR: In this paper, the modeling and simulation of a material accumulation process in micro-range based on laser-based free form heading is discussed, where the Stefan problem is coupled with the Navier-Stokes equations including a free capillary surface.
Journal ArticleDOI
Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes-Equations and Mesh Movement
TL;DR: A sharp interface model approach is taken and a quadratic tracking-type cost functional is defined that penalizes the deviation of the interface from the desired state and the control costs.
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Riccati-feedback Control of a Two-dimensional Two-phase Stefan Problem
TL;DR: The feedback control problem for a two-dimensional two-phase Stefan problem is discussed, which uses a sharp interface representation in combination with mesh-movement to track the interface position and applies the linear-quadratic regulator approach to attain a feedback control.
References
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Book ChapterDOI
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
Book
Free and moving boundary problems
TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.
Journal ArticleDOI
An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions
TL;DR: In this article, an arbitrary Lagrangian-Eulerian kinematical description of the fluid domain is adopted in which the grid points can be displaced independently of fluid motion.
Journal ArticleDOI
Local mesh refinement in 2 and 3 dimensions
TL;DR: In this paper, an algorithm for local refinement of a given conforming triangulation in 2 or 3 dimensions is presented, and the finiteness of the algorithm and stability of the obtained triangulations are given.