A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations
<|reference_start|>A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations: 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.<|reference_end|>
@article{hardy2024a,
    title={A Second Moment Method for k-Eigenvalue Acceleration with Continuous
  Diffusion and Discontinuous Transport Discretizations},
    author={Zachary K. Hardy, Jim E. Morel, Jan I.C. Vermaak},
    journal={arXiv preprint arXiv:2409.06162},
    year={2024},
    number={LA-UR-24-22251},
    archivePrefix={arXiv},
    eprint={2409.06162},
    primaryClass={math.NA cs.NA math-ph math.MP}
}