Journal Article10.13182/NSE86-A18343
A Linear Discontinuous Finite Difference Formulation for Synthetic Coarse-Mesh Few-Group Diffusion Calculations
J.M. Aragones,Carol Ahnert +1 more
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TL;DR: In this article, a linear discontinuous finite difference formulation to solve the diffusion equations in coarse mesh and few groups is developed, where the correction factors for heterogeneities, coarse mesh, and spectral effects are general interface flux discontinuity factors that can be explicitly calculated (synthetized) from detailed diffusion or transport solutions in fine mesh (heterogeneous) and multigroups, preserving the integrated fluxes and interface net currents.
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Abstract: A linear discontinuous finite difference formulation to solve the diffusion equations in coarse mesh and few groups is developed. The correction factors for heterogeneities, coarse mesh, and spectral effects are general interface flux discontinuity factors that can be explicitly calculated (synthetized) from detailed diffusion or transport solutions in fine mesh (heterogeneous) and multigroups, preserving the integrated fluxes and interface net currents. The stability is explicitly established for general synthetizations and for specific fine to coarse mesh and group reductions. Computing methods have been implemented for one-group (grey) synthetic diffusion acceleration, two-dimensional nodal/local solutions, and three-dimensional nodal simulation of pressurized water reactor cores. Results demonstrate the simplicity and stability of the formulation, a regular behaviour of the correction factors, an outstanding acceleration performance, and high potential for parallel and vector computing.
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Citations
Assembly homogenization techniques for core calculations
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Advanced PWR Core Calculation Based on Multi-group Nodal-transport Method in Three-dimensional Pin-by-Pin Geometry
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92
Leakage corrected spatial (assembly) homogenization technique
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TL;DR: In this article, a homogenization technique is developed to account for the interassembly neutron leakage effect on the homogenized parameters within generalized equivalence theory, and the method is implemented into a two-group nodal diffusion model.
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The Analytic Coarse-Mesh Finite Difference Method for Multigroup and Multidimensional Diffusion Calculations
TL;DR: In this article, the analytical coarse-mesh finite difference (ACMFD) method for multigroup diffusion equations with any number of groups and multidimensional diffusion calculations of eigenvalue and external source problems is presented.
Convergence analysis of the nonlinear coarse-mesh finite difference method for one-dimensional fixed-source neutron diffusion problem
TL;DR: The optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.
37
References
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J. H. Bramble,Richard S. Varga +1 more
Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.
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Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations
TL;DR: In this paper, a class of acceleration schemes that resemble the conventional synthetic method in that they utilize the diffusion operator in the transport iteration schemes were investigated, and the authors investigated a set of acceleration methods that are similar to the ones described in this paper.
On the Reconstruction of Local Homogeneous Neutron Flux and Current Distributions of Light Water Reactors from Nodal Schemes
K. Koebke,L. Hetzelt +1 more
TL;DR: In this paper, the reconstruction of local multigroup neutron flux and current distributions within a node is discussed for nodal light water reactor calculations, and interpolation schemes that exploit the typical...
50
Two Nodal Methods for Solving Time-Dependent Group Diffusion Equations
TL;DR: In this article, two methods for solving the transient group diffusion equations for reactors composed of large homogeneous nodal regions were developed, in which nodal coupling constants are in effect computed by an analytical method; in the second, a polynomial expansion of the flux is used.
49
Finite element method for charged-particle calculations
J. J. Honrubia,J.M. Aragones +1 more
TL;DR: In this paper, a new method for solving the Boltzmann-Fokker-Planck equation is presented, where the solution is projected onto a space defined by linear discontinuous basis functions.
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