应用数学和力学（英文版）
應用數學和力學（英文版）
응용수학화역학（영문판）
APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION)
2014年
9期
1189-1202
,共14页
high-order compact (HOC) scheme%alternative direction implicit (ADI) scheme%immersed interface method (IIM)%Richardson extrapolation 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.
