scholarly journals Development and Validation of a Three-Dimensional Diffusion Code Based on a High Order Nodal Expansion Method for Hexagonal-zGeometry

2016 ◽  
Vol 2016 ◽  
pp. 1-21 ◽  
Author(s):  
Daogang Lu ◽  
Chao Guo
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Quadratic Polynomial ◽  
Quadratic Approximation ◽  
Polynomial Expansion ◽  
Benchmark Problems ◽  
One Dimensional ◽  
Nodal Expansion Method

A three-dimensional, multigroup, diffusion code based on a high order nodal expansion method for hexagonal-zgeometry (HNHEX) was developed to perform the neutronic analysis of hexagonal-zgeometry. In this method, one-dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four-order polynomial expansion, respectively. The approximations for one-dimensional radial and axial spatially flux both have second-order accuracy. Moment weighting is used to obtain high order expansion coefficients of the polynomials of one-dimensional radial and axial spatially flux. The partially integrated radial and axial leakages are both approximated by the quadratic polynomial. The coarse-mesh rebalance method with the asymptotic source extrapolation is applied to accelerate the calculation. This code is used for calculation of effective multiplication factor, neutron flux distribution, and power distribution. The numerical calculation in this paper for three-dimensional SNR and VVER 440 benchmark problems demonstrates the accuracy of the code. In addition, the results show that the accuracy of the code is improved by applying quadratic approximation for partially integrated axial leakage and four-order approximation for one-dimensional axial spatially flux in comparison to flat approximation for partially integrated axial leakage and quadratic approximation for one-dimensional axial spatially flux.

Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

2018 ◽  
Author(s):  
Guo Chao ◽  
Liu Yu ◽  
He Hangxing ◽  
Liu Luguo ◽  
Wang Xiaoyu ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Benchmark Problems ◽  
Weighting Method ◽  
Control Rod ◽  
Order Polynomial ◽  
Runge Kutta ◽  
Nodal Expansion Method

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1

2002 ◽  
Vol 124 (4) ◽  
pp. 674-684 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Differential Equations ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Transfer Problems

A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

scholarly journals Computer modeling system for the numerical solution of the one-dimensional non-stationary Burgers’ equation

2019 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Computer Modeling ◽  
Burgers Equation ◽  
Boundary Value ◽  
Three Dimensional ◽  
Benchmark Problems ◽  
One Dimensional ◽  
Radial Basis ◽  
The One

The computer modeling system for numerical solution of the nonlinear one-dimensional non-stationary Burgers’ equation is described. The numerical solution of the Burgers’ equation is obtained by a meshless scheme using the method of partial solutions and radial basis functions. Time discretization of the one-dimensional Burgers’ equation is obtained by the generalized trapezoidal method (θ-scheme). The inverse multiquadric function is used as radial basis functions in the computer modeling system. The computer modeling system allows setting the initial conditions and boundary conditions as well as setting the source function as a coordinate- and time-dependent function for solving partial differential equation. A computer modeling system allows setting such parameters as the domain of the boundary-value problem, number of interpolation nodes, the time interval of non-stationary boundary-value problem, the time step size, the shape parameter of the radial basis function, and coefficients in the Burgers’ equation. The solution of the nonlinear one-dimensional non-stationary Burgers’ equation is visualized as a three-dimensional surface plot in the computer modeling system. The computer modeling system allows visualizing the solution of the boundary-value problem at chosen time steps as three-dimensional plots. The computational effectiveness of the computer modeling system is demonstrated by solving two benchmark problems. For solved benchmark problems, the average relative error, the average absolute error, and the maximum error have been calculated.

scholarly journals Three-dimensional time-dependent neutron diffusion simulation using average current nodal expansion method

2020 ◽  
Vol 35 (3) ◽  
pp. 189-200
Author(s):  
Kambiz Valavi ◽  
Ali Pazirandeh ◽  
Gholamreza Jahanfarnia
Keyword(s):  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Steady State Solution ◽  
Time Dependent ◽  
Test Case ◽  
Neutron Diffusion ◽  
Average Current ◽  
Coarse Meshes ◽  
Nodal Expansion Method

In this work, the average current nodal expansion method was developed for the time-dependent neutronic simulation of transients in a nuclear reactor's core. For this purpose, an adopted iterative algorithm was proposed for solving the 3-D time-dependent neutron diffusion equation. In the average current nodal expansion method, the domain of the reactor core can be modeled by coarse meshes for neutronic calculation associated with reasonable precision of results. The discretization of time differential terms in the time-dependent equations was fulfilled, according to the implicit scheme. The proposed strategy was implemented in some kinetic problems including an infinite slab reactor, TWIGL 2-D seed-blanket reactor, and 3-D LMW LWR. At first, the steady-state solution was carried out for each test case, and then, the dynamic neutronic calculation was performed during the time for a specified transient scenario. Obtained results of static and dynamic solutions were verified in comparison with well-known references. Results can indicate the ability of the developed calculator to simulate transients in a nuclear reactor's core.

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