COMPARISON OF 3 APPROXIMATIONS TO THE LINEAR-LINEAR NODAL TRANSPORT METHOD IN WEIGHTED DIAMOND-DIFFERENCE FORM

Two previously derived approximations to the linear-linear nodal transport method, the linear-nodal (LN) and the linear-linear (LL) methods, are reexamined, together with a new approximation, the bilinear (BL) method, that takes into account the bilinear nodal flux moment. The final equations are manipulated and cast in the form of the classical weighted diamond-difference (WDD) equations (not just a WDD algorithm). A computer program that solves two-dimensional transport problems using the LN, LL, or the BL method is used to solve three test problems. The results are used to confirm our algebraic manipulations of the nodal equations and also to compare the performance of three methods from the computational, as well as the theoretical, point of view. The three methods are found to have comparable accuracies for the problems studied, especially on meshes that are sufficiently fine.