A hybrid method for reactor core simulations employing finite difference and polynomial expansion with improved treatment of transverse leakage

Abstract

The paper describes a new method for the solution of the few group diffusion equations for core calculations. A combination of a polynomial expansion in the axial direction and fine mesh finite differencing in the transverse (x-y direction) directions is used in the code developed for pin by pin core calculations. A fourth order polynomial expansion is used (as in the nodal expansion method) to represent the axial flux but the expression for transverse leakage is also accurate to fourth order unlike the quadratic leakage commonly used in nodal expansion methods. Lower order polynomial representations are used to account for the possibility of axial variation of cross-sections within a mesh. This permits the use of longer and therefore fewer meshes in the z direction than in the finite difference and nodal methods. Comparisons with results of benchmark problems are presented that show that few axial meshes are adequate to obtain accurate results.