Presented By: Nuclear Engineering & Radiological Sciences
PhD Defense: Ben Yee
A Multilevel in Space and Energy Solver for Multigroup Diffusion and Coarse Mesh Finite Difference Eigenvalue Problems
Title: A Multilevel in Space and Energy Solver for Multigroup Diffusion and Coarse Mesh Finite Difference Eigenvalue Problems
Co-Chair: Prof. Edward Larsen
Co-Chair: Dr. Brendan Kochunas
Abstract: In reactor physics, the efficient solution of the multigroup neutron diffusion eigenvalue problem is desired for various applications. The diffusion problem is a lower-order but reasonably accurate approximation to the higher- fidelity multigroup neutron transport eigenvalue problem, and, in cases where the full-fidelity of the transport solution is needed, its solution can be used to accelerate the convergence of transport solvers via methods such as Coarse Mesh Finite Difference (CMFD). Although the multigroup CMFD eigenvalue problem is orders of magnitude smaller than a typical transport problem, it can still have hundreds of millions of unknowns, and obtaining its solution is not a trivial task. In the Michigan Parallel Characteristics Transport (MPACT) code, the lack of an efficient CMFD solver has resulted in a computational bottleneck at the CMFD step. Despite being a low-order accelerator, the CMFD component of MPACT can comprise 50% or more of the overall runtime when the de facto default CMFD solver in MPACT is used. Addressing this bottleneck is the motivation for our work.
The primary focus of this thesis is the theory, development, implementation, and testing of a new Multilevel-in-Space-and-Energy Diffusion (MSED) method for efficiently solving multigroup diffusion and CMFD eigenvalue problems. As its name suggests, MSED efficiently converges multigroup diffusion and CMFD problems by leveraging lower-order systems with coarsened energy and/or spatial grids. Compared to the de facto default CMFD solver, results from our implementation of MSED in MPACT show a ~8- 12x reduction in the CMFD runtime required by MPACT for single statepoint calculations on 3-D, full-core, 51-group reactor models. The number of transport sweeps is also typically reduced by the use of MSED, which is able to better converge the CMFD system than the default CMFD solver. This leads to further savings in overall runtime that is not captured by the difference in CMFD runtime.
Co-Chair: Prof. Edward Larsen
Co-Chair: Dr. Brendan Kochunas
Abstract: In reactor physics, the efficient solution of the multigroup neutron diffusion eigenvalue problem is desired for various applications. The diffusion problem is a lower-order but reasonably accurate approximation to the higher- fidelity multigroup neutron transport eigenvalue problem, and, in cases where the full-fidelity of the transport solution is needed, its solution can be used to accelerate the convergence of transport solvers via methods such as Coarse Mesh Finite Difference (CMFD). Although the multigroup CMFD eigenvalue problem is orders of magnitude smaller than a typical transport problem, it can still have hundreds of millions of unknowns, and obtaining its solution is not a trivial task. In the Michigan Parallel Characteristics Transport (MPACT) code, the lack of an efficient CMFD solver has resulted in a computational bottleneck at the CMFD step. Despite being a low-order accelerator, the CMFD component of MPACT can comprise 50% or more of the overall runtime when the de facto default CMFD solver in MPACT is used. Addressing this bottleneck is the motivation for our work.
The primary focus of this thesis is the theory, development, implementation, and testing of a new Multilevel-in-Space-and-Energy Diffusion (MSED) method for efficiently solving multigroup diffusion and CMFD eigenvalue problems. As its name suggests, MSED efficiently converges multigroup diffusion and CMFD problems by leveraging lower-order systems with coarsened energy and/or spatial grids. Compared to the de facto default CMFD solver, results from our implementation of MSED in MPACT show a ~8- 12x reduction in the CMFD runtime required by MPACT for single statepoint calculations on 3-D, full-core, 51-group reactor models. The number of transport sweeps is also typically reduced by the use of MSED, which is able to better converge the CMFD system than the default CMFD solver. This leads to further savings in overall runtime that is not captured by the difference in CMFD runtime.
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