A Unified Form of Stabilized Finite Element Methods for Solving the First-Order Neutron Transport Equation

摘要

In this summary, a unified stabilized Petrov-Galerkin finite element form for the first-order neutron transport equation has been established. This form unifies the SUPG, GLS and ASGS method. The stabilization parameter is identified as Intrinsic Free Path (IFP), and it has a great influence on the stability and convergence of the equation, we give a widely applicable stabilization parameter in this summary, but the optimal value for different methods needs more study. The results tend to converge as the element size decreases, but the oscillation phenomenon always exists for Galerkin method. The stabilized finite element methods will convergence faster and without oscillations. This method can also be applied to 2 and 3 dimensional problems.