Effective Non-oscillatory Regularized L$_1$ Finite Elements for Particle Transport Simulations

TL;DR

This paper introduces a new regularized L1 finite element method for radiation transport that effectively suppresses oscillations near discontinuities and maintains accuracy in scattering problems.

Contribution

The paper develops a novel RL1 finite element scheme with a new boundary condition, improving stability and accuracy over existing least-squares methods in particle transport simulations.

Findings

Prevents oscillations near discontinuities.

Accurately handles scattering problems.

Demonstrates stability with a new boundary condition.

Abstract

In this work, we present a novel regularized L$_1$ (RL$_1$) finite element spatial discretization scheme for radiation transport problems. We review the recently developed least-squares finite element method in nuclear applications. We then derive an L$_1$ finite element by minimizing the L$_1$ norm of the transport residual. To ensure the stability on incident boundary, we newly develop a consistent L$_1$ boundary condition (BC). The numerical tests demonstrate such a method effectively prevents the oscillations which would occur to least-squares finite element when discontinuity exists such as void and absorber. Further, the RL$_1$ method is accurate in problems with scattering.