A New High-Order Compact ADI Method for 3-D Unsteady Convection-Diffusion Problems with Discontinuous Coefficients

Abstract

In this article, a fourth-order compact alternating direction implicit (ADI) method, based on the clasical Douglas-Gunn ADI method combined with Richardson's extrapolation technique, is proposed for solving 3-D unsteady convection-diffusion equations with discontinuous coefficients. To achieve fourth-order temporal accuracy, a correction term that ensures the realization of extrapolation and reduces the splitting error is introduced. The scheme has unconditional stability and can be solved by the Thomas algorithm. Numerical experiments, including continuous/discontinuous coefficients cases, are conducted to verify the robustness and the high accuracy of this new method.

Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions, which helped us to improve the results of this article. The first author is partially supported by the Graduate Student Research Innovation Program of Xinjiang (No. XJGRI2013011) and the Excellent Doctor Innovation Program of Xinjiang University (No. XJUBSCX-2012003). The second author is partially supported by the Distinguished Young Scholars Fund of Xinjiang Province (No. 201311010), the NSF of China (No. 11271313, No. 61163027), and the Key Project of Chinese Ministry of Education (No. 212197). The third author is partially supported by the NSF of China (No. 11362021).