Application of Stiffness Confinement Method in Transient Transport Calculation

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Chuntao Tang
Keyword(s):  
Computational Efficiency ◽  
Numerical Stability ◽  
Method Of Characteristics ◽  
Original Method ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Kinetics Equation ◽  
Neutron Kinetics ◽  
Transient Transport ◽  
Transport Calculation

Abstract Stiffness confinement method (SCM) can effectively alleviate the stiffness in the neutron kinetics equation and can use larger time steps to obtain the same calculation accuracy and improve the computational efficiency. However, the existing SCM is mainly used to solve two group transient diffusion equations. In this paper, the SCM is employed to solve the multigroup transient transport calculation. On the basis of the original method of characteristics (MOC) code PEACH, the transient function is added, and the PEACH-K program is developed. Based on the numerical results of the latest published OECD/NEA C5G7-TD benchmark, it shows that the PEACH-K program developed in this paper has both high computing precision and good numerical stability.

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

The Sensitivity Simulation of Different Geometric Pretreatment in Method of Characteristics

2017 ◽  
Author(s):  
Tian XiaoRui ◽  
Zhou Tao ◽  
Li Zichao ◽  
Yu Tao
Keyword(s):  
Computational Efficiency ◽  
Method Of Characteristics ◽  
Azimuthal Angle ◽  
Reactor Core ◽  
Characteristic Line ◽  
Simulation Results ◽  
And Storage

In reactor core physics analysis,the research about the pre-processing of Method of Characteristic (MOC) including the generation and storage of characteristic line,the progress of calculation and the choosing of different quadrature set.In addition,doing some simulations,which is based on OpenMOC code and C5G7-MOX benchmark,about different parameters (including the track spacing,azimuthal angles and polar angles) and calculated its impacts on the computational efficiency and accuracy.the simulation results are as following:setting the track spacing as 0.1 cm or the azimuthal angle number as 4,the simulation results have better accuracy. Whether choosing the Leonard’s optimum quadrature set or the Tabuchi-Yamamoto quadrature set,the number of polar angles have tiny impact on accuracy.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Averaging and integral manifolds

1970 ◽  
Vol 2 (2) ◽  
pp. 197-222 ◽  
Author(s):  
W. A. Coppel ◽  
K. J. Palmer
Keyword(s):  
Autonomous System ◽  
Method Of Characteristics ◽  
Integral Manifold ◽  
Artificial Viscosity ◽  
Original Method ◽  
Method Of Averaging ◽  
System Of Differential Equations ◽  
Viscosity Term ◽  
Integral Manifolds ◽  
The Individual

An integral manifold for a system of differential equations is a manifold such that any solution of the equations which has a point on it is entirely contained on it. The method of averaging establishes the existence of such a manifold for a system which is a perturbation of an autonomous system with a periodic orbit. The existence of the manifold is established here under more general hypotheses, namely for perturbations which are ‘integrally small’. The method differs from the original method of Bogolyubov and Mitropolskii and operates directly with the individual solutions. This is made possibly by the use of an appropriate norm, and is equivalent to solving the partial differential equation which occurs in work by Moser and Sacker by the method of characteristics rather than by the introduction of an artificial viscosity term. Moreover, detailed smoothness properties of the manifold are obtained. For periodic perturbations the integral manifold is a torus and these smoothness properties are just sufficient to permit the application of Denjoy's theorem.

Influence of velocity head on filling transients in a branched pipeline

2018 ◽  
Vol 35 (7) ◽  
pp. 2502-2513 ◽  
Author(s):  
Ling Wang ◽  
Fujun Wang ◽  
Bryan William Karney ◽  
Ahmad Malekpour ◽  
Zhengwei Wang
Keyword(s):  
Method Of Characteristics ◽  
Energy Equation ◽  
Transient Flow ◽  
Numerical Results ◽  
Velocity Head ◽  
Piezometric Head ◽  
Content Type ◽  
High Point ◽  
Hydraulic Transient ◽  
Column Separation

Purpose The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head. Design/methodology/approach An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other. Findings The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes. Originality/value The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis.

scholarly journals Efficient Local Level Set Method without Reinitialization and Its Appliance to Topology Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wenhui Zhang ◽  
Yaoting Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Local Level ◽  
Band Model ◽  
Numerical Process ◽  
Local Level Set ◽  
Narrow Band Model

The local level set method (LLSM) is higher than the LSMs with global models in computational efficiency, because of the use of narrow-band model. The computational efficiency of the LLSM can be further increased by avoiding the reinitialization procedure by introducing a distance regularized equation (DRE). The numerical stability of the DRE can be ensured by a proposed conditionally stable difference scheme under reverse diffusion constraints. Nevertheless, the proposed method possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures, so that a bidirectional evolutionary algorithm based on discrete level set functions is combined with the LLSM to replace the numerical process of hole nucleation. Numerical examples are given to show high computational efficiency and numerical stability of this algorithm for topology optimization.

Thruster and FPSO Hull Interaction

2014 ◽  
Author(s):  
Ye Tian ◽  
Spyros A. Kinnas
Keyword(s):  
Experimental Data ◽  
Hybrid Method ◽  
Computational Efficiency ◽  
Vortex Lattice ◽  
Numerical Results ◽  
Navier Stokes ◽  
Dynamic Positioning ◽  
Lattice Method ◽  
Vortex Lattice Method ◽  
Number Of Cells

A hybrid method which couples a Vortex-Lattice Method (VLM) solver and a Reynolds-Averaged Navier-Stokes (RANS) solver is applied to simulate the interaction between a Dynamic Positioning (DP) thruster and an FPSO hull. The hybrid method could significantly reduce the number of cells to fifth of that in a full blown RANS simulation and thus greatly enhance the computational efficiency. The numerical results are first validated with available experimental data, and then used to assess the significance of the thruster/hull interaction in DP systems.

scholarly journals A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 966
Author(s):  
Fukang Yin ◽  
Jianping Wu ◽  
Junqiang Song ◽  
Jinhui Yang
Keyword(s):  
Computational Complexity ◽  
Error Analysis ◽  
Numerical Stability ◽  
High Order ◽  
Numerical Results ◽  
Computational Time ◽  
Legendre Transform ◽  
Practical Application ◽  
Block Partitioning ◽  
Very High

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(Nlog2N /loglogN) in theory and O(Nlog3N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

Linear Least-Squares Computations Using Givens Transformations

1983 ◽  
Vol 37 (4) ◽  
pp. 225-233 ◽  
Author(s):  
J. A. R. Blais
Keyword(s):  
Least Squares ◽  
Error Estimates ◽  
Data Storage ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Direct Method ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Estimation Problems ◽  
A Direct Method

Givens transformations provide a direct method for solving linear least-squares estimation problems without forming the normal equations. This approach has been shown to be particularly advantageous in recursive situations because of characteristics related to data storage requirements, numerical stability and computational efficiency. The following discussion will concentrate on the problem of updating least-squares parameter and error estimates using Givens transformations. Special attention will be given to photogrammetric and geodetic applications.

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