An integral equation method for spherical Stefan problems

被引：5
|
作者：
Case, Elizabeth [1 ]
Tausch, Johannes [1 ]
机构：
[1] So Methodist Univ, Dept Math, Dallas, TX 75275 USA
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 23期
基金：
美国国家科学基金会;
关键词：
Stefan problem; Spherical solidification; Laser melting; Abel integral equation; Nystrom method; NUMERICAL-SOLUTION; SOLIDIFICATION; LASER;
D O I：
10.1016/j.amc.2012.05.033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Many applications in solidification or melting are described by a two-phase Stefan problem with spherical symmetry. Using Green's representation theorem, the heat equation is reformulated as a system of integral equations for the unknown fluxes on the interface. The unknown radius of the solid-liquid interface is determined from the Stefan condition. The integral equation is discretized with the Nystrom method for which special singularity corrected quadrature rules are discussed. Numerical examples are presented that demonstrate the effectiveness of the method. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：11451 / 11460
页数：10
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