On an improved Direct Discrete Method and its application in two dimensional multi-group neutron diffusion equation

An improvement to the Direct Discrete Method (DDM), also known as the Cell Method, has been discussed. The improvement is based on a duality theorem between the primal and dual complexes. Also, the analog counterpart of the Integral operator has been derived in this paper. The multi-group neutron diffusion is then derived, directly in a discrete algebraic form, according to this procedure. A numerical example has shown that this method would yield a high order of convergence (approximately 4.6) if its parameters are adjusted suitably. Finally, the method is applied to the 2D IAEA benchmark problem, and has shown to yield accurate solutions with a reasonably low number of unknowns.

► We have examined a possible optimization to the Direct Discrete Method. ► The discrete analogs of Gradient and Integral operators is found. ► A rebalancing scheme has been approached to use the dual mesh information. ► Convergence order has been improved from 4 to 4.6 for quadratic interpolation. ► Accurate eigenvalues are found with coarse meshes.