A LINEAR CHARACTERISTIC-NODAL TRANSPORT METHOD FOR THE TWO-DIMENSIONAL, (X,Y)-GEOMETRY, MULTIGROUP DISCRETE ORDINATES EQUATIONS OVER AN ARBITRARY TRIANGLE MESH

A numerical solution to the two-dimensional (x,y)-geometry multi-group discrete ordinates transport equations over a mesh of arbitrary shaped triangles is derived. The numerical method uses the analytic solution of the discrete ordinates equations with a linear source function to generate a linear representation of the angular flux on the boundaries of the triangle. Two cases must be solved for triangular mesh cells; inflow through one face and inflow through two faces of the triangle. The one inflow side problem is solved by the linear characteristic method. The two inflow sides case is solved by the linear nodal method. The angular flux on the single outflow face is represented by a linear moment expansion. The coefficients of this expansion are obtained from the solution of the zero'th and first spatial moments of the discrete ordinates equation with a linear source representation. The linear source moments are formed by finite difference expressions of vertex source data.; The linear characteristic-nodal (LCN) method is compared against other two-dimensional spatial differencing methods for accuracy and positivity. The semi-analytic method is shown to be superior in accuracy and positivity to the diamond difference (DD) spatial schemes for all test cases. The arbitrary triangle LCN scheme is shown to be asymptotically third-order convergent for equilateral mesh problems. The LCN scheme is compared with the linear discontinuous (LD) method on equilateral triangle meshes. LD exhibited only asymptotic second-order convergence for the meshes considered, but proved more accurate in course meshes than the LCN scheme. This is thought to be due to the first-order finite differences used for calculation of the source moment terms.; From this study it is concluded that the semi-analytic LCN spatial differencing scheme is considerably more accurate and positive than DD schemes. The LCN method was found to be at least third-order convergent for the test cases examined. Further research into the effects of different source and edge flux representations on the accuracy of the method should be performed. The semi-analytic spatial differencing schemes should be implemented in production codes to gain further experience with the method.