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

doi:10.1007/s10483-014-1851-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (9): 1189-1202.doi: https://doi.org/10.1007/s10483-014-1851-6

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

刘建康^1,2, 郑洲顺^2,3

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

收稿日期:2013-04-25 修回日期:2014-01-15 出版日期:2014-09-01 发布日期:2014-09-01
通讯作者: Jian-kang LIU, liujk189@gmail.com E-mail:liujk189@gmail.com
基金资助:
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)

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

Jian-kang LIU^1,2, Zhou-shun ZHENG^2,3

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:2013-04-25 Revised:2014-01-15 Online:2014-09-01 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)

摘要/Abstract

摘要： 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.

关键词: high-order compact (HOC) scheme, alternative direction implicit (ADI) scheme, immersed interface method (IIM), Richardson extrapolation method

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.

Key words: high-order compact (HOC) scheme, alternative direction implicit (ADI) scheme, immersed interface method (IIM), Richardson extrapolation method

中图分类号:

O241.82

刘建康;郑洲顺. Efficient high-order immersed interface methods for heat equations with interfaces[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1189-1202.

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

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

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

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