|Table of Contents|

An Immersed Interface Method for One Dimensional Stefan Problems(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2018年02期
Page:
12-
Research Field:
·数学与计算机科学·
Publishing date:

Info

Title:
An Immersed Interface Method for One Dimensional Stefan Problems
Author(s):
Ji Haifeng
School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China
Keywords:
interface problemimmersed interfacemoving interface
PACS:
O242
DOI:
10.3969/j.issn.1001-4616.2018.02.003
Abstract:
This paper is considered with the immersed interface numerical methods for solving the classic one dimensional Stefan problem. Based on the grid which is independent of the moving interface,a finite different method with first order accuracy in time and second order accuracy in space is developed. Finally,some numerical examples are presented to show the accuracy of the method.

References:

[1] TADI M. A fixed-grid local method for 1-D Stefan problems[J]. Applied mathematics and computation,2012,219(4):2331-2341.
[2]SONG T,UPRETI K,SUBBARAYAN G. A sharp interface isogeometric solution to the Stefan problem[J]. Computer methods in applied mechanics and engineering,2015,284:556-582.
[3]PESKIN C S. Numerical analysis of blood flow in the heart[J]. Journal of computational physics,1977,25(3):220-252.
[4]LEVEQUE R,LI Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources[J]. SIAM J Numer Anal,1994,31(4):1019-1044.
[5]BEALE J,LAYTON A. On the accuracy of finite difference methods for elliptic problems with interfaces[J]. Communications in applied mathematics and computational science,2008,1(1):91-119.[6]LEVEQUE R,LI Z. Immersed interface methods for stokes flow with elastic boundaries or surface tension[J]. SIAM journal on scientific computing,1997,18(3):709-735.
[7]LEE L,LEVEQUE R. An immersed interface method for incompressible Navier-Stokes equations[J]. SIAM journal on scientific computing,2006,25(3):832-856.
[8]YANG X,LI B,LI Z. The immersed interface method for elasticity problems with interfaces[J]. Dynamics of continuous discrete and impulsive systems,2002,10(5):783-808.
[9]TAN Z,LE D,LI Z,et al. An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane[J]. Journal of computational physics,2008,227(23):9955-9983.
[10]TAN Z,LIM K,KHOO B. An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries[J]. Journal of computational physics,2009,228(18):6855-6881.
[11]JI H,CHEN J,LI Z. A new augmented immersed finite element method without using SVD interpolations[J]. Numerical algorithms,2016,71,395-416.

Memo

Memo:
-
Last Update: 2018-11-06