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

doi:10.1007/s10483-014-1851-6

Abstract

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

2010 MSC Number:

O241.82

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

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