Articles

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

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  • 1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P. R. China;
    2. School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China;
    3. State Key Laboratory of Porous Metal Materials, Xi'an 710016, P. R. China

Received date: 2013-04-25

  Revised date: 2014-01-15

  Online published: 2014-09-01

Supported by

Project supported by the National Natural Science Foundation of China (No. 51174236), the National Basic Research Program of China (973 Program) (No. 2011CB606306), and the Opening Project of State Key Laboratory of Porous Metal Materials (No.PMM-SKL-4-2012)

Abstract

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.

Cite this article

Jian-kang LIU;Zhou-shun ZHENG . Efficient high-order immersed interface methods for heat equations with interfaces[J]. Applied Mathematics and Mechanics, 2014 , 35(9) : 1189 -1202 . DOI: 10.1007/s10483-014-1851-6

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