scholarly journals NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

1994 ◽  
Author(s):  
P.J. Turinsky ◽  
R.M.K. Al-Chalabi ◽  
P. Engrand ◽  
H.N. Sarsour ◽  
F.X. Faure ◽  
...  
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Expansion Method ◽  
Neutron Diffusion ◽  
Transient Problems ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry

2010 ◽  
Vol 240 (8) ◽  
pp. 1997-2004 ◽  
Author(s):  
Dengying Wang ◽  
Fu Li ◽  
Jiong Guo ◽  
Jinfeng Wei ◽  
Jingyu Zhang ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Expansion Method ◽  
Cylindrical Geometry ◽  
Neutron Diffusion ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

Research on Nodal Expansion Method for Transient Convection Diffusion Equation

2014 ◽  
Author(s):  
Xiafeng Zhou ◽  
Fu Li
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Expansion Method ◽  
Neutron Diffusion ◽  
Dimensional Problem ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

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.

scholarly journals COMPARISONS AMONG THREE COUPLING FORMS OF CYLINDRICAL NODAL EXPANSION METHODS

2021 ◽  
Vol 247 ◽  
pp. 10009
Author(s):  
Yutong Wen ◽  
Ding She ◽  
Lei Shi ◽  
Jing Zhao
Keyword(s):  
High Temperature ◽  
Expansion Method ◽  
Neutron Diffusion ◽  
Coarse Mesh ◽  
Nodal Method ◽  
Coupling Equations ◽  
Partial Current ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation ◽  
High Temperature Gas

Nodal expansion method (NEM) is a typical nodal method in solving neutron diffusion equation in coarse mesh spatial discretization. NEM has been extended to cylindrical geometry in previous studies. Cylindrical NEM can be realized by different forms, where the variables in the nodal coupling equations are classified as net current, flux or partial current at the nodal surface, respectively. The three types of coupling forms of NEM have been implemented in PANGU code for the high temperature gas-cooled reactor (HTGR) physics analysis. This paper derives the three types of coupling forms of NEM, and analyzes their performance in solving the HTGR model containing void region.

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