Some improvements in solving the transport equation by the use of the family of weighted nodal schemes

An adaptive fix-up algorithm for the fourth order of accuracy linear best/quadratic continuous (LB/QC) scheme and the third order of accuracy linear discontinuous (LD) scheme, based on the use of the weighted LB/QC–weighted LD (WLB/QC-WLD) scheme is described and tested for 1D and 2D geometries case. Both the zeroth and the first spatial moment balance equations are satisfied exactly in this approach. For curvilinear geometries case a modified weighted diamond differencing (WDD) auxiliary equation in angular variable for the zeroth order spatial moments at cell angular sides is proposed that essentially improves the accuracy of the WLB/QC-WLD scheme both in k_eff calculations and in the vicinity of the sphere centrum and cylinder axis. Numerical experiment has shown that the use of the LB/QC and LD schemes supplied by the adaptive fix-up algorithm instead of, for example, the adaptive WDD (AWDD) scheme is able to improve essentially the performance of the S_N codes. (author)