Efficient high-order immersed interface methods for heat equations with interfaces

An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compa...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and mechanics 2014-09, Vol.35 (9), p.1189-1202
Main Author: 刘建康 郑洲顺
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-014-1851-6