• Nuclear Engineering and Technology
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• v.55 no.4
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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.

• Journal of Energy Engineering
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• v.17 no.4
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• pp.233-240
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• 2008

Conventionally, the second-order self-adjoint neutron transport equations have been studied using the even parity and the odd parity equations. Recently, however, the SAAF(self-adjoint angular flux) form of neutron transport equation has been introduced as a new option for the second-order self-adjoint equations. In this paper we validated the SAAF equation mathematically and clarified how it relates with the existing even and odd parity equations. We also developed a second-order SAAF differencing formula including DSA(diffusion synthetic acceleration) from the first-order difference equations. Numerical result is attached to show that the proposed methods increases accuracy with effective computational effort.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.10a
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• pp.103-108
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• 1995

By applying the P$_1$ and P$_2$ equations to the operator form of a synthetic acceleration, we derive the p,-acceleration (diffusion synthetic acceleration: DSA) and P$_2$-acceleration (p$_2$SA) schemes in one dimensional slab geometry. We Fourier-analyze the derived acceleration schemes with the discrete-ordinates transport equation and showed that the DSA outperforms the P$_2$SA. These results confirm that one cannot simply assume that replacement of the DSA with a higher order approximation will lead to a better acceleration performance.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.485-498
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• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

• Proceedings of the Korean Nuclear Society Conference
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• 2001.05a
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• pp.62-62
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• 2001

• Nuclear Engineering and Technology
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• v.41 no.4
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• pp.381-390
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• 2009

This article provides selects of outstanding problems in computational neutron transport, with some suggested approaches thereto, as follows: i) ray effect in discrete ordinates method, ii) diffusion synthetic acceleration in strongly heterogeneous problems, iii) method of characteristics extension to three-dimensional geometry, iv) fission source and $k_{eff}$ convergence in Monte Carlo, v) depletion in Monte Carlo, vi) nuclear data evaluation, and vii) uncertainty estimation, including covariance data.

• Nuclear Engineering and Technology
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• v.54 no.11
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• pp.4280-4295
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• 2022

In this paper, a new multi-group neutron-gamma transport calculation code system STRAUM-MATXST for complicated geometrical problems is introduced and its development status including numerical tests is presented. In this code system, the MATXST (MATXS-based Cross Section Processor for S_N Transport) code generates multi-group neutron and gamma cross sections by processing MATXS format libraries generated using NJOY and the STRAUM (S_N Transport for Radiation Analysis with Unstructured Meshes) code performs multi-group neutron-gamma coupled transport calculation using tetrahedral meshes. In particular, this work presents the recent implementation and its test results of the Krylov subspace methods (i.e., Bi-CGSTAB and GMRES(m)) with preconditioners using DSA (Diffusion Synthetic Acceleration) and TSA (Transport Synthetic Acceleration). In addition, the Krylov subspace methods for accelerating the energy-group coupling iteration through thermal up-scatterings are implemented with new multi-group block DSA and TSA preconditioners in STRAUM.