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

作　　者：刘建康 郑洲顺 

机构地区：[1]School of Mathematical Sciences,Shanxi University [2]School of Mathematics and Statistics,Central South University [3]State Key Laboratory of Porous Metal Materials

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第9期1189-1202,共14页应用数学和力学（英文版）

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

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.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 

分 类 号：O175[理学—数学]