Open AccessIterative solution of the diffusion and P<sub>1</sub> finite element equations
Author(s) -
E.T. Tomlinson,
James C. Robinson,
D.R. Vondy
Publication year - 1976
Language(s) - English
Resource type - Reports
DOI - 10.2172/4067391
Subject(s) - boltzmann equation , mathematics , mathematical analysis , finite element method , spherical harmonics , convergence (economics) , quadratic equation , convection–diffusion equation , acceleration , scattering , physics , geometry , classical mechanics , economics , thermodynamics , economic growth , optics , quantum mechanics
A method for obtaining solutions to the time-independent Boltzmann neutron transport equation on triangular grids with nonorthogonal boundaries and anisotropic scattering is developed. A functional is obtained from the canonical form of the multigroup transport equation. The angular variable is then removed by expanding the functional in spherical harmonics, retaining only the first two moments and limiting the anisotropic scattering to be linear. The finite element method is then implemented by using quadratic Lagrange-type interpolating polynomials to span the spatial domain. The resultant set of coupled linear equations is then solved iteratively. The applicability of convergence acceleration techniques developed for the finite difference method is tested and implemented where appropriate. Finally, a number of numerical experiments are performed to evaluate the performance of the proposed method. The results are compared to results obtained by various established methods. In all cases, agreement is excellent. 16 figures, 7 tables. (auth