A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a “preconditioning” approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presentedfor a simple model problem with a known analytical solution and for keff evaluations ofsome benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence Orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.
