Journal ArticleDOI
Finite-element methods for steady solidification problems
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TLDR
In this paper, four Galerkin finite-element methods are tested for solving the free-boundary problem that describes steady solidification, and they differ in the solution method used to account for the unknown shape of the melt/solid interface, in the interphase condition (either balance of heat flux or equilibrium of temperature) distinguished for locating the interface, and in the technique used for solving systems of algebraic equations that result from the finite element approximation.About:
This article is published in Journal of Computational Physics.The article was published on 1983-01-01. It has received 129 citations till now. The article focuses on the topics: Finite element method & Galerkin method.read more
Citations
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Creeping motion of a sphere through a Bingham plastic
TL;DR: In this article, a finite element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow, and the accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem.
Journal ArticleDOI
Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique
Gregory Ryskin,L. G. Leal +1 more
TL;DR: In this article, a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system is presented, which is also constructed numerically and always adjusted so as to fit the current boundary shape.
Journal ArticleDOI
Global modelling of heat transfer in crystal growth furnaces
TL;DR: In this article, Radiative exchanges are calculated with the assumption of diffuse surfaces and with use of a viewed and hidden part algorithm together with a Galerkin discretization.
Journal ArticleDOI
Convection and segregation in directional solidification of dilute and non-dilute binary alloys: Effects of ampoule and furnace design
TL;DR: In this paper, a Petrov-Galerkin/finite element method is used to analyze the effect of furnace configuration and ampoule design on the temperature field, the convection in the melt, the shape of the melt-solid interface, and the segregation of solute in the crystal, in the directional solidification of several dilute and nondilute binary semiconductor alloys.
Journal ArticleDOI
Finite element simulation of metal casting
Roland W. Lewis,K. Ravindran +1 more
TL;DR: Finite element algorithms for the entire casting process from the mould filling stage to the prediction of the final distorted shape are discussed in detail as discussed by the authors, with special emphasis on the coupling of the solidification analysis based on the heat conduction equation with fluid flow or thermal stress analysis.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Book
Numerical methods in finite element analysis
TL;DR: Numerical methods in finite element analysis, Numerical techniques in finite elements analysis, and so on.
Book
Vectors, Tensors and the Basic Equations of Fluid Mechanics
TL;DR: Vectors, tensors and the basic equations of fluid mechanics as discussed by the authors, Vectors and tensors, and the Basic Equations of Fluid Mechanics, and their basic equations.