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Abstract
An additional source term is an effective way to deal with boundary conditions to accelerate convergence rate, and it has been widely used in the literature. However, we find that this method has only first-order accuracy in its present form, which may decrease the accuracy of the numerical solution. A second-order additional source term method is proposed in this article, with detailed derivations. The numerical examples show that, compared to the first-order additional source term method, the second-order one has higher precision. Moreover, a unified expression is presented to treat the three common types of boundary conditions.
Acknowledgments
This study has supported by the National Science Foundation of China (No. 51176204 and No. 51134006) and the State Key Laboratory of Multiphase Flow in Power Engineering (Xi'an Jiaotong University).