A Nodal Integral Method for the Neutron Diffusion Equation in Cylindrical Geometry PDF Download
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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.
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.
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.
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."
Author: Christian Constanda Publisher: Springer Nature ISBN: 3031071719 Category : Mathematics Languages : en Pages : 361
Book Description
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
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Author: H. P. Flatt
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Author: Christian Constanda
Author: Robert Christian Penland
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