Nodal expansion method (NEM), well known for its high accuracy and efficiency, has been widely applied to reactor physics analysis. It is proven that NEM has an advantage over traditional finite difference method (FDM) and finite volume method (FVM). However, for most reactor thermal hydraulic codes, traditional FDM or FVM is still in use, and the NEM is barely utilized. Therefore, to make full use of the advantages of NEM and effectively solve the thermal hydraulic problems, the derivation and analytical process of nodal expansion method for transient convection-diffusion equation is studied in this paper. First, time discretization is derived by finite difference method, and then is manipulated to ensure that the form of convection-diffusion equation is consistent with that of neutron diffusion equation. After that, the approach of NEM for neutron diffusion equation can be easily utilized in the thermal hydraulic codes, and the code TNEM based on NEM is developed to solve the multi-dimensional transient convection-diffusion equation. At last, through the numerical benchmarks and error analysis, the numerical results of TNEM are found to agree well with the reference solutions and are superior to that of center difference scheme and first order upwind scheme as for the one-dimensional problem and multi-dimensional problem. Furthermore, good accuracy can be maintained even for coarse meshes.

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