一维Stefan问题的二阶差分格式(英文)  

A SECOND ORDER DIFFERENCE SCHEME FOR ONE-DIMENSIONAL STEFAN PROBLEM

作　　者：王加玲 孙志忠[2] 

机构地区：[1]陆军指挥学院,南京210045 [2]东南大学数学系,南京210096

出　　处：《南京大学学报（数学半年刊）》2010年第2期218-229,共12页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by Natural Science Foundation of China(Grant Number 10871044)

摘　　要：本文考虑经典的一维Stefan问题的数值求解.借助于Landau变换,构造了一个三层线性化Crank-Nicolson型差分格式来确定温度分布和动边界的位置.用能量分析方法证明了差分格式的唯一可解性。数值例子说明了差分格式的无条件稳定性和二阶收敛性.This article is concerned with the numerical solution of the classical one dimensional phase Stefan problem.A Landon-type transformation is introduced to make the problem on a fixed domain.A new function transformation is introduced to make the nonlinear boundary condition be a linear one.A linearized three-level difference scheme of Crank-Nicolson-type is constructed to determine the temperature distribution and the position of the moving boundary.The unique solvability of the difference scheme is proved by the energy method.A numerical example is presented to demonstrate the unconditional stability and second-order convergence of the finite difference scheme.

关 键 词：STEFAN问题 Landau变换 差分格式 唯一可解性 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]