Analysis and Optimization of Implicit Methods for Time-Dependent Transport Calculations of Source-Driven Systems

Abstract

The numerical solution of the time-dependent neutron transport equation is considered for subcritical source-driven systems. In the first part of the work, the properties of the time-implicit discretization scheme are examined by means of a time-harmonic analysis. The separate effects of the time and space-angle discretizations are considered in order to show the different errors due to each approximation. The dependence of the error on the characteristic parameters of the problem is discussed. In the second part of the paper, a novel modified diffusion-acceleration method is proposed for the time-implicit discretized transport equation. The new technique provides accurate results with substantially lower computational cost.

KEYWORDS:

• subcritical source-driven systems
• neutron transport theory
• neutron transport
• time dependence
• numerical solutions
• errors
• accuracy
• diffusion-acceleration method
• transport theory