On Some Nonlinear Extentions of Askew Coarse Mesh Method

Abstract

The extended Askew coarse mesh method is a well-known nonlinear method of solving multigroup, multidimensional neutron diffusion equation of a nuclear reactor. However, its reliability is not sufficient—because of its nonlinearity, such nonphysical results as negative neutron fluxes and complex-valued neutron multiplication factor may be encountered, the iterative processes may diverge, and so on. To avoid these difficulties called solvability crisis of the nonlinear extended Askew coarse mesh method, in the present article, new extensions of Askew's method are investigated. In the suggested method, τ _ri ,τ _zi variables are chosen by an optimization, in particular, on condition of excluding the solvability crisis. The new method is an extension of the previous method for τ _ri ,τ _zi ≠ 3, and the new method reproduces the old one with τ _ri = τ _zi = 3. Sufficient conditions of existence of positive solution for the new method are given. It is proved, in particular, that a choice of parameters 4/τ _ri + 2/τ _zi ≤ 1 ensures positive solvability of the corresponding equations of the generalized method in three-dimensional hexagonal geometry.

Keywords:

• Nuclear reactor
• Diffusion equation
• Nonlinear coarse mesh method