1 A higher-order bounded discretization scheme

2010 ◽  
pp. 3-18
Author(s):  
Baojun Song ◽  
Ryo S. Amano
Keyword(s):  
Higher Order ◽  
Discretization Scheme

Effect of the Accuracy Order of the Discretization Scheme on the Prediction Performance for the Turbulent Flow Structure Inside Fuel Assembly: Sensitivity Study

2015 ◽  
Author(s):  
Gong Hee Lee ◽  
Ae Ju Cheong
Keyword(s):  
Turbulent Flow ◽  
Fuel Assembly ◽  
Flow Structure ◽  
Sensitivity Study ◽  
Higher Order ◽  
Discretization Scheme ◽  
Order Of Accuracy ◽  
Accuracy Order ◽  
Turbulent Flow Structure ◽  
Numerical Order

Spatial discretization errors result from both the numerical order of accuracy of the discretization scheme, and from grid spacing. It is well known that second, or higher, order discretization schemes are potentially able to produce high-quality solutions. In addition, when either the flow is not aligned with the grid, or is complex, it is recommended that the first order discretization scheme not be used for the convection term, if possible. However, the higher-order scheme can also result in convergence difficulties and instabilities at certain flow conditions. In this study, to examine the effect of the numerical order of accuracy of the discretization scheme on the prediction accuracy for the turbulent flow structure inside fuel assembly with the split-type mixing vanes, simulations were conducted with the commercial CFD (Computational Fluid Dynamics) software, ANSYS CFX R.14. Two different types of the discretization scheme for the convection-terms-of-momentum and -turbulence equations, i.e. 1st order upwind scheme and a high resolution scheme, were used. The predicted results were compared with the measured data from MATiS-H (Measurement and Analysis of Turbulent Mixing in Subchannles-Horizontal) facility, installed in the KAERI (Korea Atomic Energy Research Institute).

scholarly journals Simulation of cracks in linear elastic solids using higher order Particle Discretization Scheme-FEM

2015 ◽  
Vol 71 (2) ◽  
pp. I_327-I_337 ◽  
Author(s):  
Mahendra Kumar PAL ◽  
Lalith WIJERATHNE ◽  
Muneo HORI ◽  
Tsuyoshi ICHIMURA
Keyword(s):  
Higher Order ◽  
Discretization Scheme ◽  
Elastic Solids ◽  
Linear Elastic

High order weak approximation for irregular functionals of time-inhomogeneous SDEs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toshihiro Yamada
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximation Method ◽  
Numerical Experiments ◽  
Higher Order ◽  
High Order ◽  
Weak Approximation ◽  
Discretization Scheme ◽  
Unified Approach

Abstract This paper shows a general weak approximation method for time-inhomogeneous stochastic differential equations (SDEs) using Malliavin weights. A unified approach is introduced to construct a higher order discretization scheme for expectations of non-smooth functionals of solutions of time-inhomogeneous SDEs. Numerical experiments show the validity of the method.

scholarly journals Implementation of Finite Element Method with Higher Order Particle Discretization Scheme

2014 ◽  
Vol 70 (2) ◽  
pp. I_297-I_305 ◽  
Author(s):  
Mahendra Kumar PAL ◽  
Lalith WIJERATHNE ◽  
Muneo HORI ◽  
Tsuyoshi ICHIMURA ◽  
Seizo TANAKA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Higher Order ◽  
Discretization Scheme ◽  
Element Method

On a higher-order bounded discretization scheme

2000 ◽  
Vol 32 (7) ◽  
pp. 881-897 ◽  
Author(s):  
B. Song ◽  
G. R. Liu ◽  
K. Y. Lam ◽  
R. S. Amano
Keyword(s):  
Higher Order ◽  
Discretization Scheme

Numerical Modeling of Brittle Cracks Using Higher Order Particle Discretization Scheme–FEM

2019 ◽  
Vol 16 (04) ◽  
pp. 1843006 ◽  
Author(s):  
Mahendra Kumar Pal ◽  
M. L. L. Wijerathne ◽  
Muneo Hori
Keyword(s):  
Target Function ◽  
Crack Tip ◽  
Higher Order ◽  
Benchmark Problems ◽  
Mode I ◽  
Mode I Crack ◽  
Discretization Scheme ◽  
Elastic Solids ◽  
Crack Problems ◽  
Local Approximations

Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM framework (HO-PDS-FEM) and applications in efficiently simulating cracks are presented in this paper. PDS is an approximation scheme which uses a conjugate domain tessellation pair like Voronoi and Delaunay in approximating a function and its derivatives. In approximating a function (or derivatives), HO-PDS first produces local polynomial approximations for the target function (or derivatives) within each element of respective tessellation. The approximations over the whole domain are then obtained by taking the union of those respective local approximations. These approximations are inherently discontinuous along the boundaries of the respective tessellation elements since the support of the local approximations is confined to the domain of respective tessellation elements and no continuity conditions are enforced. HO-PDS-FEM utilizes these inherent discontinuities in function approximation to efficiently model discontinuities such as cracks. Higher order PDS is implemented in FEM framework to solve boundary value problem of elastic solids, including mode-I crack problems. With several benchmark problems, it is shown that HO-PDS-FEM has higher expected accuracy and convergence rate. J-integral around a mode-I crack tip is calculated to demonstrate the improvement in the accuracy of the crack tip stress field. Further, it is shown that HO-PDS-FEM significantly improves the traction along the crack surfaces, compared to the zeroth-order PDS-FEM [Hori, M., Oguni, K. and Sakaguchi, H. [2005] “Proposal of FEM implemented with particle discretization scheme for analysis of failure phenomena,” J. Mech. Phys. Solids 53, 681–703].

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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