On the Choice of a Maximal Cluster in the Cluster Variational Method

1992 ◽  
Vol 291 ◽  
Author(s):  
David A. Vul ◽  
Didier de Fontaine
Keyword(s):  
Variational Method ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Cluster Variational Method ◽  
Maximal Clusters

ABSTRACTAn explanation of the occurrence of unphysical solutions in the cluster variational method is given. A simple algorithm for the construction of an optimal maximal cluster, i.e., a cluster that guarantees correct results for any set of interatomic interactions, is suggested. Examples of optimal maximal clusters for various two- and three-dimensional lattices are presented.

Laminar Fluid Flow Around Two Wall-Mounted Blocks of Different Size

2009 ◽  
Author(s):  
Mohammad Mehdi Tavakol ◽  
Mohammad Eslami
Keyword(s):  
Fluid Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Bluff Bodies ◽  
Wake Region ◽  
Science And Engineering ◽  
Vortical Structures ◽  
Laminar Fluid Flow ◽  
Pressure Distributions

Fluid flow around single or multiple bluff bodies mounted on a surface has great significance in science and engineering. Understanding the characteristics of different vortices formed around wall-mounted bodies is quite necessary for different applications. Although the case of a single surface mounted cube has been studied extensively, only little attention has been paid to the flow around two or more rectangular blocks in array. Therefore, a CFD code is developed to calculate three dimensional steady state laminar fluid flow around two cuboids of arbitrary size and configuration mounted on a surface in free stream conditions. The employed numerical scheme is finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Results are presented for two rectangular blocks of the different size mounted on a surface in various inline arrangements. Streamlines are plotted for blocks of different size ratio. Velocity and pressure distributions are also plotted in the wake region behind the obstacles. It is shown that how the behavior of flow field and vortical structures depend on the respective size and location of the larger block in comparison with the case of two inline wall mounted cubes of the same size.

Synthetic reflection seismograms in three dimensions by a locked‐mode approximation

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 350-358 ◽  
Author(s):  
G. Nolet ◽  
R. Sleeman ◽  
V. Nijhof ◽  
B. L. N. Kennett
Keyword(s):  
Finite Difference ◽  
Born Approximation ◽  
Large Scale ◽  
Layered Medium ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Realistic Model ◽  
Three Dimensions ◽  
Acoustic Response ◽  
Many Sources

We present a simple algorithm for computing the acoustic response of a layered structure containing three‐dimensional (3-D) irregularities, using a locked‐mode approach and the Born approximation. The effects of anelasticity are incorporated by use of Rayleigh’s principle. The method is particularly attractive at somewhat larger offsets, but computations for near‐source offsets are stable as well, due to the introduction of anelastic damping. Calculations can be done on small minicomputers. The algorithm developed in this paper can be used to calculate the response of complicated models in three dimensions. It is more efficient than any other method whenever many sources are involved. The results are useful for modeling, as well as for generating test signals for data processing with realistic, model‐induced “noise.” Also, this approach provides an alternative to 2-D finite‐difference calculations that is efficient enough for application to large‐scale inverse problems. The method is illustrated by application to a simple 3-D structure in a layered medium.

Three-dimensional computational study in a corrugated pipe inserted system filled with phase change material

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ömer Akbal ◽  
Hakan F. Öztop ◽  
Nidal H. Abu-Hamdeh
Keyword(s):  
Phase Change ◽  
Phase Change Material ◽  
Computational Analysis ◽  
Computational Study ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Melting Time ◽  
Geometrical Parameters ◽  
Content Type ◽  
Change Material

Purpose The purpose of this paper is to make a three-dimensional computational analysis of melting in corrugated pipe inserted system filled with phase change material (PCM). The system was heated from the inner pipe, and temperature of the outer pipe was lower than that of inner pipe. Different geometrical ratio cases and two different temperature differences were tested for their effect on melting time. Design/methodology/approach A computational analysis through a pipe with corrugated pipe filled with PCM is analyzed. Finite volume method was applied with the SIMPLE algorithm method to solve the governing equations. Findings The results indicate that the geometrical parameters can be used to control the melting time inside the heat exchanger which, in turn, affect the energy efficiency. The fastest melting time is seen in Case 4 at the same temperature difference which is the major observation of the current work. Originality/value Originality of this work is to perform a three-dimensional analysis of melting of PCM in a corrugated pipe inserted pipe.

scholarly journals Applicability of Formwork Automation Design Software for Aluminum Formwork

2020 ◽  
Vol 10 (24) ◽  
pp. 9029
Author(s):  
Bokyeong Lee ◽  
Hyeonggil Choi ◽  
Byongwang Min ◽  
Dong-Eun Lee
Keyword(s):  
Computer Aided Design ◽  
Building Information Modeling ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Information Modeling ◽  
Two Dimensional ◽  
Building Information ◽  
Design Software ◽  
Modeling Data ◽  
Aided Design

In this study, by applying the developed formwork automation design software to three target structures, we reviewed the applicability of the formwork automation design software for the aluminum formwork. To apply the formwork automation design software, we built an aluminum formwork library based on the conversion of two-dimensional (2D) computer-aided design (CAD) data to three-dimensional building information modeling data for all the components of the aluminum formwork. The results of the automated formwork layout on the target structures using the formwork automation design software confirmed that the wall and deck members were laid out by the set algorithm according to the formwork size and direction. However, because of the limited functionality of the software, the level of completion of the formwork layout was found to be lower than that of the manual formwork layout based on 2D CAD data. The currently developed software is based on a simple algorithm, but has a drawback in that the automated layout is limited to only some of its members. Therefore, additional research should be conducted on the development of advanced software through the diversification of the algorithm, automation of preprocessing of the mesh, and analysis of the relationships of all the members comprising the formwork.

An efficient coupled pressure–velocity solver for three-dimensional injection molding simulation using Schur complement preconditioned FGMRES

2019 ◽  
Vol 36 (4) ◽  
pp. 1101-1120
Author(s):  
Xiang Liu ◽  
Fei Guo ◽  
Yun Zhang ◽  
Junjie Liang ◽  
Dequn Li ◽  
...  
Keyword(s):  
Injection Molding ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Schur Complement ◽  
Gradient Term ◽  
Content Type ◽  
Coupled Problem ◽  
Parallel Performance ◽  
Injection Molding Simulation ◽  
Fully Coupled

Purpose The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation. Design/methodology/approach A fully coupled pressure–velocity algorithm is developed to solve the coupled problem, by treating the pressure gradient term implicitly. And, the Schur complement preconditioned FGMRES is applied to decompose the resulting coupled pressure–velocity equation into pressure and velocity subsystems. Then, BoomerAMG is adopted to solve the pressure subsystem, and block Jacobi preconditioned FGMRES is applied to the velocity subsystem. Findings According to the several experiments, the fully coupled pressure–velocity algorithm was demonstrated to have faster convergence than the traditional SIMPLE algorithm, and the calculating time was reduced by up to 70 per cent. And, the Schur complement preconditioned FGMRES worked more efficiently than block Gauss–Seidel preconditioned FGMRES, block-selective AMG and AMG with block ILU(0) smoother and could take at least 47.4 per cent less time. The proposed solver had good scalability for different-size problems, including various cases with different numbers of elements. It also kept good speedup and efficiency in parallel performance. Originality/value A coupled solver has been proposed to effectively solve the coupled problem in the three-dimensional injection molding simulation, which is more robust and efficient than existing methods.

scholarly journals Numerical Study of the Internal Flow Field of a Centrifugal Impeller

1994 ◽  
Author(s):  
Mou-jin Zhang ◽  
Chuan-gang Gu ◽  
Yong-miao Miao
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Internal Flow ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
High Reynolds

The complex three-dimensional flow field in a centrifugal impeller with low speed is studied in this paper. Coupled with high–Reynolds–number k–ε turbulence model, the fully three–dimensional Reynolds averaged Navier–Stokes equations are solved. The Semi–Implicit Method for Pressure–Linked Equations (SIMPLE) algorithm is used. And the non–staggered grid arrangement is also used. The computed results are compared with the available experimental data. The comparison shows good agreement.

scholarly journals Computation of the Jet-Wake Flow Structure in a Low Speed Centrifugal Impeller

1988 ◽  
Author(s):  
B. L. Lapworth ◽  
R. L. Elder
Keyword(s):  
Three Dimensional ◽  
Simple Algorithm ◽  
Design Flow ◽  
Wake Flow ◽  
Staggered Grid ◽  
Centrifugal Impeller ◽  
Low Speed ◽  
Flow Equations ◽  
System A ◽  
Speed Flow

The low speed flow through the shrouded de-Havilland Ghost centrifugal impeller is computed using an incompressible elliptic calculation procedure. The three dimensional viscous flow equations are solved using the SIMPLE algorithm in an arbitrary generalised coordinate system. A non-staggered grid arrangement is implemented in which pressure oscillations are eliminated using an amended pressure correction scheme. Flow computations are performed at ‘nominal’ low speed design and above design flow rates, and (on the coarse grids used in the calculations) good agreement is obtained with the experimentally observed jet-wake structure of the flow.

scholarly journals Variational method for the three-dimensional many-electron dynamics of semiconductor quantum wells

2012 ◽  
Author(s):  
Fernando Haas ◽  
Padma K. Shukla ◽  
José Tito Mendonça ◽  
Bengt Eliasson ◽  
David Resedes
Keyword(s):  
Variational Method ◽  
Quantum Wells ◽  
Three Dimensional ◽  
Electron Dynamics ◽  
Semiconductor Quantum Wells
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