Moment closures based on minimizing the residual of the PN angular expansion in radiation transport

JOURNAL OF COMPUTATIONAL PHYSICS

卷:314

Article

Zheng, Weixiong¹  McClarren, Ryan G.¹ 

[1] Texas A&M Univ, Nucl Engn, College Stn, TX 77843 USA

关键词: Spherical harmonics closures;    Radiation transport;   

DOI  :  10.1016/j.jcp.2016.03.030

来源: Elsevier

【 摘 要 】

In this work we present two new closures for the spherical harmonics (P-N) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard truncation and diffusive closures do not minimize the residual of the P-N expansion. Based on this analysis we derive two models, a moment-limited diffusive (MLDN) closure and a transient P-N (TPN) closure that attempt to address shortcomings of common closures. The form of these closures is similar to flux-limiters for diffusion with the addition of a time-derivative in the definition of the closure. Numerical results on a pulsed plane source problem, the Gordian knot of slab-geometry transport problems, indicate that our new closure outperforms existing linear closures. Additionally, on a deep penetration problem we demonstrate that the TPN closure does not suffer from the artificial shocks that can arise in the M-N entropybased closure. Finally, results for Reed's problem demonstrate that the TPN solution is as accurate as the PN+3 solution. We further extend the TPN closure to 2D Cartesian geometry. The line source test problem demonstrates the model effectively damps oscillations and negative densities. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free