Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
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.
Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
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.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
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.
Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in Cylindrical Geometry
A Nodal Integral Method for the Neutron Diffusion Equation in Cylindrical Geometry
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This Summary reports recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical, r-z, geometry. Comparisons of numerical solutions to two test problems with those obtained by the code EXTERMINATOR-2 indicate the superior accuracy of the nodal integral method solutions on much coarser meshes. 6 refs., 1 fig., 1 tab.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This Summary reports recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical, r-z, geometry. Comparisons of numerical solutions to two test problems with those obtained by the code EXTERMINATOR-2 indicate the superior accuracy of the nodal integral method solutions on much coarser meshes. 6 refs., 1 fig., 1 tab.
Nuclear Science Abstracts
Energy Research Abstracts
Nuclear Science Abstracts
Handbook of Nuclear Engineering
Author: Dan Gabriel Cacuci
Publisher: Springer Science & Business Media
ISBN: 0387981306
Category : Science
Languages : en
Pages : 3701
Book Description
This is an authoritative compilation of information regarding methods and data used in all phases of nuclear engineering. Addressing nuclear engineers and scientists at all levels, this book provides a condensed reference on nuclear engineering since 1958.
Publisher: Springer Science & Business Media
ISBN: 0387981306
Category : Science
Languages : en
Pages : 3701
Book Description
This is an authoritative compilation of information regarding methods and data used in all phases of nuclear engineering. Addressing nuclear engineers and scientists at all levels, this book provides a condensed reference on nuclear engineering since 1958.
ERDA Energy Research Abstracts
Author: United States. Energy Research and Development Administration
Publisher:
ISBN:
Category : Medicine
Languages : en
Pages : 776
Book Description
Publisher:
ISBN:
Category : Medicine
Languages : en
Pages : 776
Book Description
Finite Difference Approximations to the Neutron Diffusion Equation
Author: H. P. Flatt
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 40
Book Description
The finite difference approximations used in several one-dimensional neutron diffusion codes are studied from the point of view of conservation of neutrons. A new set of approximation formulae is proposed which conserve neutrons. These formulae differ only slightly from earlier formulae, thus allowing a small effect to be corrected by a small amount of effort."
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 40
Book Description
The finite difference approximations used in several one-dimensional neutron diffusion codes are studied from the point of view of conservation of neutrons. A new set of approximation formulae is proposed which conserve neutrons. These formulae differ only slightly from earlier formulae, thus allowing a small effect to be corrected by a small amount of effort."
Transactions of the American Nuclear Society
Author: American Nuclear Society
Publisher:
ISBN:
Category : Nuclear engineering
Languages : en
Pages : 1096
Book Description
Publisher:
ISBN:
Category : Nuclear engineering
Languages : en
Pages : 1096
Book Description