VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

doi:10.2172/4158202

Cited by 23 publications

(13 citation statements)

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“…Table 1 gives the results of our calculations. Compared to heterogeneous VENTURE 17) finite-difference solution, the maximum errors in the assembly power density are only 0.59% and 1.17%, respectively, for the analytic and semi-analytic calculations. The analytic result is appreciably more accurate than semi-analytic result.…”

Section: Oecd-l336 (C5) Benchmark Problemmentioning

confidence: 90%

Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations

Cho

2002

Journal of Nuclear Science and Technology

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Two advanced nodal methods for the solution of the multigroup neutron diffusion equations are developed, using the nonlinear coarse-mesh finite difference (CMFD) scheme. Based on the analytic and semi-analytic methods, the relationships between the flux and current on the nodal surface are derived, by which the two-node problem is formulated in an efficient way. The issue of the complex eigenmodes and the instability problem inherent in the analytic solution are considered in order to have an efficient and stable algorithm. The numerical results demonstrate the effectiveness of the two methods.

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Section: Oecd-l336 (C5) Benchmark Problemmentioning

confidence: 90%

Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations

Cho

2002

Journal of Nuclear Science and Technology

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“…The resulting equation system can be solved with well known iteration techniques including different acceleration methods such as successive over relaxation and others. The finite difference methods are used in the codes PDQ-7 (Cadwell, 1967), VENTURE (Vondy et al, 1977) and CITATION (Fowler, 1999).…”

Section: Finite Difference Methodsmentioning

confidence: 99%

Development of a parallel analytic coarse mesh finite difference code for two group diffusion equation solution in two dimensional rectangular geometries

Hosseini

Khalafi

Khakshornia

2015

Progress in Nuclear Energy

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“…The neutron diffusion equation for one-dimension plane geometry can be written as follows: (12) where u is the flux we want to know, S is the source distribution, and others are standard. For the neutron diffusion Eq.…”

Section: One-dimensional Heterogeneous Plane Geometry Problemmentioning

confidence: 99%

Wavelet-Based Algorithms for Solving Neutron Diffusion Equations

Nasif¹,

Omori²,

Suzuki³

et al. 2001

Journal of Nuclear Science and Technology

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This work develops efficient algorithms for numerically solving the neutron diffusion equation by a wavelet Galerkin method (WGM). One of the main problems encountered in solving neutron diffusion equation using WGM is the treatment of the boundary and interface conditions. In one-dimensional problems, the boundaries of the wavelet series expansions are assumed to be the analytical boundaries of the problem, and the boundary condition equations are replaced by end equations in Galerkin system. In two-dimensional problems, in order to maintain the integrity of the system, the boundaries of the wavelet series are shifted until the end is independent on any expansion coefficients of the scaling function that affect the solution within the real boundaries.Since the scaling functions are compactly supported, only a finite number of the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily, therefore, enables us to extend the solution to two-dimensional heterogeneous cases and make the inner iteration efficient in the eigenvalue and multigroup problems. We tested our WGM algorithm with several diffusion problems including two-dimensional heterogeneous problems and multi-group problems. The solutions are very accurate with a proper selection of Daubechies' order and dilation order. Our WGM algorithm provides very accurate solutions for one-dimensional and two-dimensional heterogeneous problems in which the flux exhibits very steep gradients.

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VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

Cited by 23 publications

References 0 publications

Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations

Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations

Development of a parallel analytic coarse mesh finite difference code for two group diffusion equation solution in two dimensional rectangular geometries

Wavelet-Based Algorithms for Solving Neutron Diffusion Equations

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