High-Order Lax-Friedrichs WENO Fast Sweeping Methods for the S_N Neutron Transport Equation

Fast sweeping methods are efficient iterative techniques originally developed to solve the steady-state Hamilton-Jacobi equations and later used for the hyperbolic conservation laws. For these boundary value problems, their solution information propagates along characteristics starting from the boundary. These fast sweeping methods take advantage of this property and achieve very fast convergence based on a Gauss-Seidel–type iteration approach and alternating-direction sweeping strategy. In this paper, we solve the S_N neutron transport equation using the high-order Lax-Friedrichs Weighted Essentially Non-Oscillatory (LF-WENO) fast sweeping methods. Our numerical tests in one and two dimensions demonstrate that the proposed new sweeping methods can achieve better accuracy and positivity preserving than the diamond difference method for the S_N solution.