Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations

2005 ◽  
Vol 151 (3) ◽  
pp. 274-282 ◽  
Author(s):  
Akio Yamamoto
Keyword(s):  
Neutron Transport ◽  
Coarse Mesh

scholarly journals A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 424
Author(s):  
Dean Wang ◽  
Zuolong Zhu
Keyword(s):  
Fourier Analysis ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Successive Overrelaxation ◽  
Computational Cell ◽  
Artificial Diffusion ◽  
Acceleration Method ◽  
The Stability ◽  
Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

Performance, Accuracy and Efficiency Evaluation of a Three-Dimensional Whole-Core Neutron Transport Code AGENT

2006 ◽  
Author(s):  
Tatjana Jevremovic ◽  
Mathieu Hursin ◽  
Nader Satvat ◽  
John Hopkins ◽  
Shanjie Xiao ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Open Architecture ◽  
Coarse Mesh ◽  
Research Reactors ◽  
Acceleration Techniques ◽  
Performance Accuracy ◽  
Transport Code ◽  
Neutron Propagation

The AGENT (Arbitrary GEometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) the theory of R-functions used to generate real three-dimensional whole-cores of square, hexagonal or triangular cross sections, (2) the planar method of characteristics used to solve isotropic neutron transport in non-homogenized 2D) reactor slices, and (3) the one-dimensional diffusion theory used to couple the planar and axial neutron tracks through the transverse leakage and angular mesh-wise flux values. The R-function-geometrical module allows a sequential building of the layers of geometry and automatic submeshing based on the network of domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through a set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: Coarse Mesh Rebalancing (CMR) and Coarse Mesh Finite Difference (CMFD). The stand-alone originally developed graphical user interface of the AGENT code design environment allows the user to view and verify input data by displaying the geometry and material distribution. The user can also view the output data such as three-dimensional maps of the energy-dependent mesh-wise scalar flux, reaction rate and power peaking factor. The AGENT code is in a process of an extensive and rigorous testing for various reactor types through the evaluation of its performance (ability to model any reactor geometry type), accuracy (in comparison with Monte Carlo results and other deterministic solutions or experimental data) and efficiency (computational speed that is directly determined by the mathematical and numerical solution to the iterative approach of the flux convergence). This paper outlines main aspects of the theories unified into the AGENT code formalism and demonstrates the code performance, accuracy and efficiency using few representative examples. The AGENT code is a main part of the so called virtual reactor system developed for numerical simulations of research reactors. Few illustrative examples of the web interface are briefly outlined.

Development of a Two-Dimensional Modularity Characteristics Code for Neutron Transport Calculation

2013 ◽  
Author(s):  
Liang Liang ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Youqi Zheng
Keyword(s):  
Large Scale ◽  
Method Of Characteristics ◽  
Neutron Transport ◽  
Engineering Application ◽  
Polar Angle ◽  
Two Dimensional ◽  
Coarse Mesh ◽  
Characteristics Method ◽  
Large Scale Problems ◽  
Transport Calculation

The method of characteristics (MOC) has been widely used in lattice code for its high precision and easy complement. However, the long characteristics method needs large quantity of PC memory when dealing with large scale problems. The modularity MOC method could significantly reduce the PC memory when calculating the problem which contains lots of repeatedly geometries, like the fuel assembly in the reactor. In this method, only typical geometric cells are selected to trace the rays, and then the geometry information of these cells is stored. So, the modularity MOC method is feasible to perform well in the calculation with large scale. When tracing the rays, the technique of mesh ray generating and the corresponding azimuthal quadrature set are both applied. The techniques make sure that each ray has the reflected ray in the boundary so it is convenient to describe the boundary condition. The optimal polar angle and the Guass quadrature set are selected as the polar quadrature set. Furthermore, the coarse mesh finite difference (CMFD) is employed to accelerate the calculation. A pin cell is chosen as the coarse mesh. The CMFD solution provides the MOC with much faster converged fission and scattering source distributions. The LOTUS code is developed and the numerical results show that the code is precise for engineering application and the CMFD acceleration is effective.

scholarly journals MULTILEVEL CMFD ACCELERATION METHODS FOR WHOLE CORE REACTOR SIMULATION IN VERA

2021 ◽  
Vol 247 ◽  
pp. 02037
Author(s):  
Luke Cornejo ◽  
Benjamin Collins ◽  
Shane Stimpson
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Virtual Environment ◽  
Difference Method ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Reactor Physics ◽  
Acceleration Methods ◽  
Solver Performance ◽  
Full Core

Ongoing efforts are being made to improve the performance of MPACT as the deterministic neutron transport solver in the Virtual Environment for Reactor Analysis (VERA). As other parts of the code have been improved, the coarse mesh finite difference method (CMFD) has come to take up a significant portion of the runtime. Multilevel-in-energy CMFD and multilevel-in-space CMFD solvers have been used to improve CMFD solver performance. A new multilevel-in-space-and-energy CMFD solver is being introduced that combines components of these two methods. W-Cycles and partial W-Cycles are being investigated to further improve the efficiency of the multilevel-in-energy CMFD solver. The performance of these methods is demonstrated on full core reactor physics problems of interest to VERA.

scholarly journals DEMONSTRATION OF A LINEAR PROLONGATION CMFD METHOD ON MOC

2021 ◽  
Vol 247 ◽  
pp. 03006
Author(s):  
Jin Li ◽  
Yunlin Xu ◽  
Dean Wang ◽  
Qicang Shen ◽  
Brendan Kochunas ◽  
...  
Keyword(s):  
Neutron Transport ◽  
Coarse Mesh ◽  
Scalar Flux ◽  
Scalar Fluxes ◽  
Transport Calculation ◽  
Discontinuity Problem ◽  
Neutron Transport Equations ◽  
The Stability ◽  
Partial Current ◽  
Better Than

Coarse Mesh Finite Difference (CMFD) method is a very effective method to accelerate the iterations for neutron transport calculation. But it can degrade and even fail when the optical thickness of the mesh becomes large. Therefore several methods, including partial current-based CMFD (pCMFD) and optimally diffusive CMFD (odCMFD), have been proposed to stabilize the conventional CMFD method. Recently, a category of “higherorder” prolongation CMFD (hpCMFD) methods was proposed to use both the local and neighboring coarse mesh fluxes to update the fine cell flux, which can solve the fine cell scalar flux discontinuity problem between the fine cells at the bounary of the coarse mesh. One of the hpCMFD methods, refered as lpCMFD, was proposed to use a linear prolongation to update the fine cell scalar fluxes. Method of Characteristics (MOC) is a very popular method to solve neutron transport equations. In this paper, lpCMFD is applied on the MOC code MPACT for a variety of fine meshes. A track-based centroids calculation method is introduced to find the centroids coordinates for random shapes of fine cells. And the numerical results of a 2D C5G7 problem are provided to demonstrate the stability and efficiency of lpCMFD method on MOC. It shows that lpCMFD can stabilize the CMFD iterations in MOC method effectively and lpCMFD method performs better than odCMFD on reducing the outer MOC iterations.

scholarly journals The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

2021 ◽  
Vol 8 (3A) ◽  
Author(s):  
Jesús Pérez Curbelo ◽  
Rafael Barbosa Libotte ◽  
Amaury Muñoz Oliva ◽  
Ricardo Carvalho Barros ◽  
Hermes Alves Filho
Keyword(s):  
Neutron Transport ◽  
Iteration Scheme ◽  
Discrete Ordinates ◽  
Coarse Mesh ◽  
Neutron Transport Equation ◽  
Balance Equations ◽  
Deterministic Method ◽  
New Approach ◽  
One Dimensional ◽  
Typical Model

A new approach for the application of the coarse–mesh Modified Spectral Deterministic method to numerically solve the two–dimensional neutron transport equation in the discrete ordinates (Sn) formulation is presented in this work. The method is based on within node general solution of the conventional one–dimensional Sn transverse integrated equations considering constant approximations for the transverse leakage terms and obtaining the Sn spatial balance equations. The discretized equations are solved by using a modified Source Iteration scheme without additional approximations since the average angular fluxes are computed analytically in each iteration. The numerical algorithm of the method presented here is algebraically simpler than other spectral nodal methods in the literature for the type of problems we have considered. Numerical results to two typical model problems are presented to test the accuracy of the offered method.

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