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Article
Publication date: 4 February 2021

Xiao Jiang and Tat Leung Chan

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

Abstract

Purpose

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

Design/methodology/approach

The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.

Findings

Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.

Originality Value

Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 4 January 2021

Carlos Enrique Torres-Aguilar, Pedro Moreno-Bernal, Jesús Xamán, Ivett Zavala Guillen and Irving Osiris Hernández-López

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and…

Abstract

Purpose

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and high-resolution schemes by the relaxation coefficients optimization.

Design methodology/approach

The objective function minimizes the residual value difference between iterations in each control volume until its difference is lower than the convergence criterion. The EA approach is evaluated in two configurations, a two-dimensional cavity with scattering media and absorbing media.

Findings

Experimental results show the capacity to obtain the numerical solution for both cases on all interpolation schemes tested by the EA approach. The EA approach reduces CPU time for the RTE numerical solution using SUPERBEE, SWEBY and MUSCL schemes until 97% and 135% in scattering and absorbing media cases, respectively. The relaxation coefficients optimized every two numerical solution iterations achieve a significant reduction of the CPU time compared to the deferred correction procedure with fixed relaxation coefficients.

Originality/value

The proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 13 July 2020

Mohammad Ali Taghikhani and Zahra Taghikhani

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations…

Abstract

Purpose

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

Design/methodology/approach

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

Findings

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

Practical implications

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Originality/value

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 17 June 2020

Tiago Oliveira, Wilber Vélez and Artur Portela

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Abstract

Purpose

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Design/methodology/approach

In the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.

Findings

The reduced integration, performed by this linearly integrated formulation, plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy and, which is most important, presents no instabilities, unlike nodal integration methods without stabilization. As a consequence of using such a convenient linearly integrated local form, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. Three benchmark problems were analyzed with these techniques, in order to assess the accuracy and efficiency of the new integrated local formulations of meshfree and finite element numerical methods. The results obtained in this work are in perfect agreement with those of the available analytical solutions and, furthermore, outperform the computational efficiency of other methods. Thus, the accuracy and efficiency of the local numerical methods presented in this paper make this a very reliable and robust formulation.

Originality/value

Presentation of a new local mesh-free numerical method. The method, linearly integrated along the boundary of the local domain, implements an algorithm with no further integration required. The method is absolutely reliable, with remarkably-accurate results. The method is quite robust, with extremely-fast computations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 16 June 2020

Paragmoni Kalita, Anoop K. Dass and Jongki Hazarika

The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are…

Abstract

Purpose

The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are generally accompanied by relatively large numerical diffusion. However, it is desirable to control the numerical diffusion of FVS schemes inside the boundary layer for improved accuracy in viscous flow computations. This study aims to develop a new methodology for controlling the numerical diffusion of FVS schemes for viscous flow computations with the help of a recently developed boundary layer sensor.

Design/methodology/approach

The governing equations are solved using a cell-centered finite volume approach and Euler time integration. The gradients in the viscous fluxes are evaluated by applying the Green’s theorem. For the inviscid fluxes, a new approach is introduced, where the original upwind formulation of an FVS scheme is first cast into an equivalent central discretization along with a numerical diffusion term. Subsequently, the numerical diffusion is scaled down by using a novel scaling function that operates based on a boundary layer sensor. The effectiveness of the approach is demonstrated by applying the same on van Leer’s FVS and AUSM schemes. The resulting schemes are named as Diffusion-Regulated van Leer’s FVS-Viscous (DRvLFV) and Diffusion-Regulated AUSM-Viscous (DRAUSMV) schemes.

Findings

The numerical tests show that the DRvLFV scheme shows significant improvement over its parent scheme in resolving the skin friction and wall heat flux profiles. The DRAUSMV scheme is also found marginally more accurate than its parent scheme. However, stability requirements limit the scaling down of only the numerical diffusion term corresponding to the acoustic part of the AUSM scheme.

Originality/value

To the best of the authors’ knowledge, this is the first successful attempt to regulate the numerical diffusion of FVS schemes inside boundary layers by applying a novel scaling function to their artificial viscosity forms. The new methodology can reduce the erroneous smearing of boundary layers by FVS schemes in high-speed flow applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 8 January 2020

Ante Džolan, Mladen Kožul, Alen Harapin and Dragan Ćubela

This paper aims to present an approach for the numerical simulation of concrete shrinkage. First, some physical mechanisms of shrinkage are described and then the…

Abstract

Purpose

This paper aims to present an approach for the numerical simulation of concrete shrinkage. First, some physical mechanisms of shrinkage are described and then the developed numerical model for the analysis of shrinkage of spatial three-dimensional structures using thermal analogy is presented. Results of the real behavior of structures because of concrete shrinkage using the developed numerical model are compared with the experimental and it is clearly shown that the developed numerical model is an efficient tool in predicting the time-dependent behavior of all concrete structures.

Design/methodology/approach

In this paper, Fib Model Code 2010 to predict shrinkage deformation of concrete is used, and it was incorporated in the three-dimensional numerical model using the thermal analogy. Mentioned three-dimensional numerical model uses the modified Rankine material law to describe concrete behavior in tension and modified Mohr-Coulomb material law to describe concrete behavior in compression. The developed three-dimensional numerical model successfully analyzes the behavior of reinforced and/or prestressed concrete structures including time-dependent deformations of concrete as well.

Findings

Results are shown in this paper clearly demonstrate the reliability of the developed numerical model in predicting the shrinkage strain, as well as its impact on concrete and reinforced concrete structures. The results obtained using the developed numerical model are in better agreement with the experimental results, than the results obtained using the numerical models from literature that also use the Fib Model Code 2010 to predict the shrinkage strain. So, it can be concluded that for a real simulation of concrete structures, alongside the model for predicting the shrinkage strain, the models for concrete behavior in tension and compression have a very important role.

Originality/value

Results of the developed three-dimensional numerical model were compared with experimental results from literature and with theoretical foundations, and it can be talked that this numerical model presents a good tool for analysis of reinforced and prestressed concrete structures including shrinkage deformation of concrete. Results obtained using the developed three-dimensional numerical model are better agreed with experimental than results of other numerical model from literature.

Details

Engineering Computations, vol. 37 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 9 November 2015

Muhammad Azim bin Azizi, Ahmad Kamal Ariffin bin Mohd Ihsan and Nik Abdullah bin Nik Mohamed

The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters…

Abstract

Purpose

The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method.

Design/methodology/approach

A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data.

Findings

The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters.

Research limitations/implications

The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper.

Practical implications

The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss.

Originality/value

The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 October 2004

Shihe Xin, Marie‐Christine Duluc, François Lusseyran and Patrick Le Quéré

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that…

Abstract

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 18 September 2009

Q. Du, D.G. Eskin and L. Katgerman

The purpose of this paper is to investigate the ways to diminish or eliminate numerical diffusion and dispersion. Numerical dispersion and diffusion are present in the…

Abstract

Purpose

The purpose of this paper is to investigate the ways to diminish or eliminate numerical diffusion and dispersion. Numerical dispersion and diffusion are present in the predicted macrosegregation profiles reported in the literature and they hinder the interpretation of the simulation results. With the motivation to eliminate these numerical problems by employing appropriate meshes, simulations of macrosegregation in a billet direct‐chill cast from a multi‐component aluminium alloy has been performed.

Design/methodology/approach

First the idea that numerical dispersion could be alleviated by refining the structured mesh size is tested and the extent of this mesh refining to overcome these numerical problems is discussed. Second the link of numerical dispersion and diffusion to the type of mesh used is investigated.

Findings

Unstructured mesh eliminates the numerical dispersion present in the structured mesh while it introduces the numerical diffusion. It is concluded by performing calculations with the same settings but different meshes that, although refining the structured mesh could alleviate the numerical oscillation, it increases the computation time dramatically. Therefore the best solution to overcome these numerical problems is the employment of a hybrid mesh consisting of both structured and unstructured mesh.

Originality/value

This work reveals the reasons behind the numerical dispersion and diffusion in macrosegregation modelling and gives a practical solution.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 2005

Chongbin Zhao, B.E. Hobbs, A. Ord, Ge Lin and H.B. Mühlhaus

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat…

Abstract

Purpose

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities in the lithosphere and crust scales.

Design/methodology/approach

The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts.

Findings

From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive‐and‐advective lithosphere with variable pore‐fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere.

Originality/value

The present analytical solutions can be used to: validate numerical methods for solving large‐scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large‐scale heat transfer problems with temperature‐dependent fluid densities.

Details

Engineering Computations, vol. 22 no. 2
Type: Research Article
ISSN: 0264-4401

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