• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• Nuclear Engineering and Technology
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• 제55권9호
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• pp.3301-3312
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• 2023

This study incorporates a high-fidelity transient analysis solver based on multigroup CMFD in the MOC code STREAM. Transport modeling with heterogeneous geometries of the reactor core increases computational cost in terms of memory and time, whereas the multigroup CMFD reduces the computational cost. The reactor condition does not change at every time step, which is a vital point for the utilization of CMFD. CMFD correction factors are updated from the transport solution whenever the reactor core condition changes, and the simulation continues until the end. The transport solution is adjusted once CMFD achieves the solution. The flux-weighted method is used for rod decusping to update the partially inserted control rod cell material, which maintains the solution's stability. A smaller time-step size is needed to obtain an accurate solution, which increases the computational cost. The adaptive step-size control algorithm is robust for controlling the time step size. This algorithm is based on local errors and has the potential capability to accept or reject the solution. Several numerical problems are selected to analyze the performance and numerical accuracy of parallel computing, rod decusping, and adaptive time step control. Lastly, a typical pressurized LWR was chosen to study the rod-ejection accident.

• Nuclear Engineering and Technology
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• 제55권4호
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• pp.1428-1438
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• 2023

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is developed and implemented as a part of a hybrid neutronics method for source convergence acceleration and variance reduction in Monte Carlo (MC) criticality calculations. The acceleration of the MC calculation stems from constructing a synthetic operator and solving a low-order problem using information obtained from previous MC calculations. By applying the P₁ approximation, two correction terms, one for the scalar flux and the other for the current, can be solved in the low-order problem and applied to the transport solution. A variety of one-dimensional (1-D) and two-dimensional (2-D) numerical tests are constructed to demonstrate the performance of FDSA in comparison with the standalone MC method and the coupled MC and Coarse Mesh Finite Difference (MC-CMFD) method on both intended purposes. The comparison results show that the acceleration by a factor of 3-10 can be expected for source convergence and the reduction in MC variance is comparable to CMFD in both slab and full core geometries, although the effectiveness of such hybrid methods is limited to systems with small dominance ratios.

• Nuclear Engineering and Technology
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• 제19권1호
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• pp.34-41
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• 1987

본 논문은 부하추종운전노심의 1차원 해석방법과 3차원 해석방법을 비교하기 위한 것이다. 이 목적으로 본 논문에서는 유한차분법에 의거한 1차원 HLOFO 코드와 수정형 Borresen 소격모형에 의한 3차원 CMSNAC 코드를 개발했다. CMSNAC 코드는 100-50-100% 출력변화를 수반하는 12-3-6-3 부하추종운전에 대한 고리 1호기 노심의 3차원 출려분포와 반응도 변수를 계산하는데 이용했다. 3차원 계산결과는 중성자속.체적 가증법으로 구한 단면적 및 버클링 입력에 의거한 1차원적 HLOFO 계산결과와 비교되었으며, 이 비교로부터 1차원 HLOFO 계산이 정착도 면에서 다소 뒤떨어지지만 3차원 계산에 가까운 결과를 얻을 수 있다는 것을 보였다.

• Nuclear Engineering and Technology
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• 제52권2호
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• pp.230-237
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• 2020

In this part, an implicit time dependent solution is presented for the Boltzmann transport equation discretized by the analytic coarse mesh finite difference method (ACMFD) over the spatial domain as well as the simplified P₃ (SP₃) for the angular variable. In the first part of this work we proposed a SP₃-ACMFD approach to solve the static eigenvalue equations which provide the initial conditions for temp dependent equations. Having solved the 3D multi-group SP₃-ACMFD static equations, an implicit approach is resorted to ensure stability of time steps. An exponential behavior is assumed in transverse integrated equations to establish a relationship between flux moments and currents. Also, analytic integration is benefited for the time-dependent solution of precursor concentration equations. Finally, a multi-channel one-phase thermal hydraulic model is coupled to the proposed methodology. Transient equations are then solved at each step using the GMRES technique. To show the sufficiency of proposed transient SP₃-ACMFD approximation for a full core analysis, a comparison is made using transport peers as the reference. To further demonstrate superiority, results are compared with a 3D multi-group transient diffusion solver developed as a byproduct of this work. Outcomes confirm that the idea can be considered as an economic interim approach which is superior to the diffusion approximation, and comparable with transport in results.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2230-2245
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• 2023

KANT (KAIST Advanced Nuclear Tachygraphy) is a PWR core simulator recently developed at Korea Advance Institute of Science and Technology, which solves three-dimensional steady-state and transient multigroup neutron diffusion equations under Cartesian geometries alongside the incorporation of thermal-hydraulics feedback effect for multi-physics calculation. It utilizes the standard Nodal Expansion Method (NEM) accelerated with various Coarse Mesh Finite Difference (CMFD) methods for neutronics calculation. For thermal-hydraulics (TH) calculation, a single-phase flow model and a one-dimensional cylindrical fuel rod heat conduction model are employed. The time-dependent neutronics and TH calculations are numerically solved through an implicit Euler scheme, where a detailed coupling strategy is presented in this paper alongside a description of nodal equivalence, macroscopic depletion, and pin power reconstruction. For validation of the steady, transient, and depletion calculation with pin power reconstruction capacity of KANT, solutions for various benchmark problems are presented. The IAEA 3-D PWR and 4-group KOEBERG problems were considered for the steady-state reactor benchmark problem. For transient calculations, LMW (Lagenbuch, Maurer and Werner) LWR and NEACRP 3-D PWR benchmarks were solved, where the latter problem includes thermal-hydraulics feedback. For macroscopic depletion with pin power reconstruction, a small PWR problem modified with KAIST benchmark model was solved. For validation of the multi-physics analysis capability of KANT concerning large-sized PWRs, the BEAVRS Cycle1 benchmark has been considered. It was found that KANT solutions are accurate and consistent compared to other published works.