Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry

Technical Report · Mon Apr 01 00:00:00 EST 2002

DOI:https://doi.org/10.2172/910654· OSTI ID:910654

Ougouag, Abderrafi Mohammed-El-Ami; Terry, William Knox

The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by “transverse integration” of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain onedimensional solutions for the neutron fluxes averaged over the other two dimensions. These solutions are found in regions (“nodes”) small enough for the material properties and cross sections in them to be adequately represented by average values. Because the solution in each node is an exact analytical solution, the nodes can be much larger than the mesh elements used in finite-difference solutions. Then the solutions in the different nodes are coupled by applying interface conditions, ultimately fixing the solutions to the external boundary conditions.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: DOE - EM
• DOE Contract Number: AC07-99ID13727
• OSTI ID: 910654
• Report Number(s): INEEL/EXT-02-00489
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
CARTESIAN COORDINATES
CROSS SECTIONS
Cylindrical Geometry
DIFFERENTIAL EQUATIONS
DIMENSIONS
GEOMETRY
Neutron Diffusion Equation
NEUTRONS
Nodal
PARTIAL DIFFERENTIAL EQUATIONS