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A New Nodal Expansion Method with High-Order Moments for the Reduction of Numerical Oscillation in Convection-Diffusion Problems

Xiafeng Zhou, Jiong Guo, Fu Li

Nuclear Science and Engineering / Volume 183 / Number 2 / June 2016 / Pages 185-195

Technical Paper /

First Online Publication:May 25, 2016
Updated:June 6, 2016

The nodal integral method (NIM) has been widely used to solve multidimensional steady-state convection-diffusion problems. However, unphysical oscillating behavior arises when NIM is applied to steep-gradient problems and discontinuous problems. In this paper, a new nodal expansion method (NEM) with high-order moments (NEM_HM) is developed to reduce the numerical oscillation drawback of NIM. High-order moments of transverse-integrated variables are introduced. Based on the definition of Legendre moments, all the expansion coefficients of NEM_HM can be defined as shared moments and unshared moments. Then, the calculation framework of the traditional NEM is extended to include the high-order moments. Additional nodal balance equations are introduced to ensure the uniqueness of all the shared variables such as node-average variables. Finally, coupled discrete equations are obtained in terms of various order moments on the surfaces of the nodes. The classical Smith-Hutton problem and a cross-flow problem are chosen to test the effectiveness of NEM_HM. Numerical results show that the accuracy of NEM_HM outperforms NIM for steep-gradient problems and discontinuous cases.