Universal methodology for statistical error and convergence of correlated Monte Carlo tallies

Ueki, Taro

Nuclear Science and Engineering, 193(7), p.776 - 789, 2019/07

https://doi.org/10.1080/00295639.2018.1562779

It is known that the convergence of standardized time series (STS) to Brownian bridge yields standard deviation estimators of the sample mean of correlated Monte Carlo tallies. In this work, a difference scheme based on a stochastic differential equation is applied to STS in order to obtain a new functional statistic (NFS) that converges to Brownian motion (BM). As a result, statistical error estimation improves twofold. First, the application of orthonormal weighting to NFS yields a new set of asymptotically unbiased standard deviation estimators of sample mean. It is not necessary to store tallies once the updating of estimator computation is finished at each generation. Second, it becomes possible to assess the convergence of sample mean in an assumption-free manner by way of the comparison of power spectra of NFS and BM. The methodology is demonstrated for three different types of problems encountered in Monte Carlo criticality calculation.

Waveform relaxation methods for second order linear differential equations

Yamada, Susumu

JAERI-Data/Code 2001-024, 18 Pages, 2001/08

JAERI-Data-Code-2001-024.pdf:0.83MB

no abstracts in English

A Development of simulation and analytical program for through-diffusion experiments for a single layer of diffusion media

Sato, Haruo

JNC TN8410 2001-003, 40 Pages, 2001/01

JNC-TN8410-2001-003.pdf:1.13MB

A program (TDROCK1.FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual.

Sympletic integrators for nonlinear Schrdinger equation

Sasa, Narimasa; Yoshida, Haruo*

Nihon Oyo Suri Gakkai Rombunshi, 10(2), p.119 - 131, 2000/06

http://ci.nii.ac.jp/naid/110001883488

no abstracts in English

Structured grid generator on parallel computers

Muramatsu, Kazuhiro; Murakami, Hiroyuki*; Higashida, Akihiro*; *

JAERI-Data/Code 97-005, 42 Pages, 1997/03

JAERI-Data-Code-97-005.pdf:1.51MB

no abstracts in English

Study of thermal-hydraulic analyses with CIP method

PNC TN9420 96-057, 48 Pages, 1996/09

PNC-TN9420-96-057.pdf:1.24MB

New type of numerical scheme CIP has been proposed for solving hyperbolic type equations and the CIP is focused on as a less numerical diffusive scheme. C-CUP method with the CIP scheme is adopted to numerical simulations that treat compressible and incompressible fluids, phase change phenomena and Mixture fluids. To evaluate applicabilities of the CIP scheme and C-CUP method for thermal hydraulic analyses related to Fast Breeder Reactors (FBRs), the scheme and the method were reviewed. Feature of the CIP scheme and procedure of the C-CUP method were presented. The CIP scheme is used to solve linear hyperbolic type equations for advection term in basic equations of fluids. Key issues of the scheme is that profile between grid points is described to solve the equation by cubic polynomial and spatial derivatives of the polynomial. The scheme can capture steep change of solution and suppress numerical error. In the C-CUP method, the basic equations of fluids are divided into advection terms and the other terms. The advection terms is solved with CIP scheme and the other terms is solved with difference method.The C-CUP method is robust for numerical instability, but mass of fluid will be in unfair preservation with non-conservative equations for fluids. Numerical analyses with the CIP scheme and the C-CUP method has been performed for phase change, mixture and moving object. These analyses are depend on characteristics of that the scheme and the method are robust for steep change of density and useful for interface tracking.