Mathematical foundations of the three-dimensional neutron hydrodynamics coupled transport equations

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.

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Concurrent Source Iteration in the Solution of Three-Dimensional, Multigroup Discrete Ordinates Neutron Transport Equations

Nuclear Science and Engineering ◽

10.13182/nse96-a24166 ◽

1996 ◽

Vol 122 (3) ◽

pp. 287-308 ◽

Cited By ~ 9

Author(s):

Milo R. Dorr ◽

Charles H. Still

Keyword(s):

Neutron Transport ◽

Three Dimensional ◽

Transport Equations ◽

Discrete Ordinates ◽

Neutron Transport Equations

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A Numerical Method for Predicting the Pressure History of a Sonic Boom Wave Incident on Arbitrarily Oriented Plane Walls

Journal of Applied Mechanics ◽

10.1115/1.3408714 ◽

1970 ◽

Vol 37 (4) ◽

pp. 889-894 ◽

Cited By ~ 1

Author(s):

B. M. Rao ◽

G. W. Zumwalt

Keyword(s):

Numerical Method ◽

Three Dimensional ◽

Artificial Viscosity ◽

Oklahoma City ◽

Sonic Boom ◽

Transient Wave ◽

Pressure History ◽

History Of ◽

Mathematical Foundations ◽

Wave Problems

The conservation laws for a plane fluid flow were simplified by the weak wave approximations valid for sonic boom-type waves and applied to a field of mesh points, utilizing the “artificial viscosity” concept for numerical stability. The numerical analysis was applied to predict the pressure history of the sonic boom wave on the window of a commercial store building in Oklahoma City which was broken during a sonic boom test in 1964. The results were compared with the results of a two-dimensional analytical method which was developed earlier by the authors and which rests on firm physical and mathematical foundations. Agreement was very good. The numerical method is not limited to plane cases but should be capable of extension to three-dimensional transient wave problems.

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