A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

TL;DR

This paper extends the second moment method for k-eigenvalue acceleration to complex reactor problems, demonstrating improved computational efficiency and robustness over existing methods using advanced discretization techniques.

Contribution

It introduces the application of the second moment method to realistic reactor problems with modern discretizations, showing its advantages over traditional acceleration schemes.

Findings

More computationally efficient on complex reactor problems

Demonstrates robustness with unstructured meshes

Comparable or better performance than quasi-diffusion

Abstract

The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasi-diffusion. While this method has been shown to be comparable to quasi-diffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to thought that the resulting inhomogeneous source makes the problem ill-posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasi-diffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.