Multigroup diffusion equations

Derivation of the Fermi age equation. The Boltzmann equation is an integro-dififerential equation involving distance, energy and directional variables. By making suitable approximations we shall now proceed to reduce this equation to a set of coupled differential equations in which the spatial coordinates are the only independent variables. These are the so-called multigroup diffusion equations. But first we discuss the so-caUed age theory. 

The interface conditions associated with the multigroup diffusion equations are generally written in the form... 

Here djdn denotes the derivative in the direction normal to the interface.) To the best of our knowledge these interface conditions have not been derived from the fundamental interface condition (2.3) and the hypotheses already made in deriving the multigroup diffusion equations (except in the very important special case of one-dimensional geometry). To illustrate the difficulties we substitute the condition (3.1) into equation (2.3) and find that... 

In order to solve a particular reactor problem it is generally necessary to adjoin to the multigroup diffusion equations (4.2) another equation which describes the thermal neutron fiux, since this is generally required for a determination of the fission sources 8j, This extra equation is taken to be of... 

G. J. Habetler and M. A. Martino, The multigroup diffusion equations of reactor physics. Report KAPL-1886, General Electric Co., Knolls Atomic Power Lab., 1958. 

G. Goertzel, M. M. Shapiro and H. S. Wilf, The numerical integration of the multigroup diffusion equation, NDA Document (no date). 

NUMERICAL METHODS FOR SOLVING MULTI-DIMENSIONAL MULTIGROUP DIFFUSION EQUATIONS... 

We shall concentrate on surveying the available numerical methods for solving the multi-dimensional multigroup diffusion equations. Since Dr. Ehrlich has already sketched the numerical methods available for treating the case of one space variable, we shall therefore concentrate on the cases of several space variables, although in general our theoretical discussions will be phrased independently of the number of space variables. In all cases we shall attempt to discuss both the rigorous mathematical features and the practical applications of these various numerical methods to both the time independent and time dependent diffusion equations. 

For the time independent multigroup diffusion equations, we have... 

MULTI-DIMENSIONAL MULTIGROUP DIFFUSION EQUATIONS 181 and p = cosh i (2/5 — 1). To start the process, and... 

Iterative methods for time dependent multigroup diffusion equations. 

The numerical solution of time dependent multigroup diffusion equations has not yet received as much attention as the number of numerical techniques, which are presently available for such problems, would suggest. We now consider the time dependent multigroup diffusion equations with an external source... 

R. S. Varga and M. A. Martino, The theory for the numerical solution of time-dependent and time-independent multigroup diffusion equations. Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958, vol. 16, pp. 570-577. 

The methods and codes applied to solve the 2D and 3D multigroup diffusion equation are well established. Most of the codes used for fast reactor analysis are based on the finite difference equation, although very efficient diffusion codes also exist using other kinds of solutions, such as finite element [4.43], coarse mesh [4.44] and nodal methods [4.45]. One of the main advantages of... 

HEXG - A center mesh finite defference code to solve multigroup diffusion equations in two dimensional hexagonal geometry. V Jagannathan and R.P. Jain. Bhabha Atomic Research Center, Bombay, India, 1989... 

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