A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914950460473344 |
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| author | Hardy, Zachary K. Morel, Jim E. Vermaak, Jan I. C. |
| author_facet | Hardy, Zachary K. Morel, Jim E. Vermaak, Jan I. C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations Hardy, Zachary K. Morel, Jim E. Vermaak, Jan I. C. Numerical Analysis Mathematical Physics 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. |
| title | A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2409.06162 |