FINITE-ELEMENT METHOD FOR NEUTRON-TRANSPORT .3. TWO-DIMENSIONAL ONE-GROUP TEST PROBLEMS

The even-parity transport equation for an isotropic scattering medium is applied using a maximum principle to determine the angular flux in a square lattice cell with a cylindrical fuel element, a square isotropic source in a corner of an absorbing shield and a dog-leg duct through an absorbing shield. The finite element solutions obtained are compared with an exact solution for the cell, and benchmark results for the square source and duct problem. The accuracies achieved for the fluxes in the cell problem are everywhere better than 0.75% and high accuracy is achieved for the other test problems. The linear elements, used for the spatial dependence of the angular flux in conjunction with a spherical harmonic expansion for the angular dependence, provide a flexible means of treating awkward geometries. At present the equations are assembled and solved using the UNCLE code, which uses direct Gaussian elimination. This process limits the speed of the finite element method to about 1 3 of the Fletcher finite difference spherical harmonics method for the square source problem. This latter method is, however, limited to systems with geometries defined by co-ordinate surfaces, whereas the finite element method can be used for any region that can be triangulated. © 1979.