## Abstract

The numerical solution of the neutron diffusion equation plays a very important role in the analysis of nuclear reactors. A wide variety of numerical procedures has been proposed, at which most of the frequently used numerical methods are fundamentally based on the finite- difference approximation where the partial derivatives are approximated by the finite difference. For complex geometries, typical of the practical reactor problems, the computational accuracy of the finite-difference method is seriously affected by the size of the mesh width relative to the neutron diffusion length and by the heterogeneity of the medium. Thus, a very large number of mesh points are generally required to obtain a reasonably accurate approximate solution of the multi-dimensional diffusion equation. Since the computation time is approximately proportional to the number of mesh points, a detailed multidimensional analysis, based on the conventional finite-difference method, is still expensive even with modern large-scale computers. Accordingly, there is a strong incentive to develop alternatives that can reduce the number of mesh-points and still retain accuracy. One of the promising alternatives is the finite element method, which consists of the expansion of the neutron flux by piecewise polynomials. One of the advantages of this procedure is its flexibility
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## Citation Formats

Lieberoth, J.
Coarse mesh code development.
NEA: N. p.,
1975.
Web.

Lieberoth, J.
Coarse mesh code development.
NEA.

Lieberoth, J.
1975.
"Coarse mesh code development."
NEA.

@misc{etde_1352886,

title = {Coarse mesh code development}

author = {Lieberoth, J.}

abstractNote = {The numerical solution of the neutron diffusion equation plays a very important role in the analysis of nuclear reactors. A wide variety of numerical procedures has been proposed, at which most of the frequently used numerical methods are fundamentally based on the finite- difference approximation where the partial derivatives are approximated by the finite difference. For complex geometries, typical of the practical reactor problems, the computational accuracy of the finite-difference method is seriously affected by the size of the mesh width relative to the neutron diffusion length and by the heterogeneity of the medium. Thus, a very large number of mesh points are generally required to obtain a reasonably accurate approximate solution of the multi-dimensional diffusion equation. Since the computation time is approximately proportional to the number of mesh points, a detailed multidimensional analysis, based on the conventional finite-difference method, is still expensive even with modern large-scale computers. Accordingly, there is a strong incentive to develop alternatives that can reduce the number of mesh-points and still retain accuracy. One of the promising alternatives is the finite element method, which consists of the expansion of the neutron flux by piecewise polynomials. One of the advantages of this procedure is its flexibility in selecting the locations of the mesh points and the degree of the expansion polynomial. The small number of mesh points of the coarse grid enables to store the results of several of the least outer iterations and to calculate well extrapolated values of them by comfortable formalisms. This holds especially if only one energy distribution of fission neutrons is assumed for all fission processes in the reactor, because the whole information of an outer iteration is contained in a field of fission rates which has the size of all mesh points of the coarse grid.}

place = {NEA}

year = {1975}

month = {Jun}

}

title = {Coarse mesh code development}

author = {Lieberoth, J.}

abstractNote = {The numerical solution of the neutron diffusion equation plays a very important role in the analysis of nuclear reactors. A wide variety of numerical procedures has been proposed, at which most of the frequently used numerical methods are fundamentally based on the finite- difference approximation where the partial derivatives are approximated by the finite difference. For complex geometries, typical of the practical reactor problems, the computational accuracy of the finite-difference method is seriously affected by the size of the mesh width relative to the neutron diffusion length and by the heterogeneity of the medium. Thus, a very large number of mesh points are generally required to obtain a reasonably accurate approximate solution of the multi-dimensional diffusion equation. Since the computation time is approximately proportional to the number of mesh points, a detailed multidimensional analysis, based on the conventional finite-difference method, is still expensive even with modern large-scale computers. Accordingly, there is a strong incentive to develop alternatives that can reduce the number of mesh-points and still retain accuracy. One of the promising alternatives is the finite element method, which consists of the expansion of the neutron flux by piecewise polynomials. One of the advantages of this procedure is its flexibility in selecting the locations of the mesh points and the degree of the expansion polynomial. The small number of mesh points of the coarse grid enables to store the results of several of the least outer iterations and to calculate well extrapolated values of them by comfortable formalisms. This holds especially if only one energy distribution of fission neutrons is assumed for all fission processes in the reactor, because the whole information of an outer iteration is contained in a field of fission rates which has the size of all mesh points of the coarse grid.}

place = {NEA}

year = {1975}

month = {Jun}

}