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Article
Publication date: 25 October 2022

David Tae and Kumar K. Tamma

The purpose of this paper is to describe a novel implementation of a multispatial method, multitime-scheme subdomain differential algebraic equation (DAE) framework allowing a mix…

Abstract

Purpose

The purpose of this paper is to describe a novel implementation of a multispatial method, multitime-scheme subdomain differential algebraic equation (DAE) framework allowing a mix of different space discretization methods and different time schemes by a robust generalized single step single solve (GS4) family of linear multistep (LMS) algorithms on a single body analysis for the first-order nonlinear transient systems.

Design/methodology/approach

This proposed method allows the coupling of different numerical methods, such as the finite element method and particle methods, and different implicit and/or explicit algorithms in each subdomain into a single analysis with the GS4 framework. The DAE, which constrains both space and time in multi-subdomain analysis, combined with the GS4 framework ensures the second-order time accuracy in all primary variables and Lagrange multiplier. With the appropriate GS4 parameters, the algorithmic temperature rate variable shift can be matched for all time steps using the DAE. The proposed method is used to solve various combinations of spatial methods and time schemes between subdomains in a single analysis of nonlinear first-order system problems.

Findings

The proposed method is capable of coupling different spatial methods for multiple subdomains and different implicit/explicit time integration schemes in the GS4 framework while sustaining second-order time accuracy.

Originality/value

Traditional approaches do not permit such robust and flexible coupling features. The proposed framework encompasses most of the LMS methods that are second-order time accurate and unconditionally stable.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 February 1996

Tianhong Ouyang and Kumar K. Tamma

Thermal solidification processes are an important concern in today’smanufacturing technology. Because of the complex geometric nature ofreal‐world problems, analytical techniques…

Abstract

Thermal solidification processes are an important concern in today’s manufacturing technology. Because of the complex geometric nature of real‐world problems, analytical techniques with closed‐form solutions are scarce and/or not feasible. As a consequence, various numerical techniques have been employed for the numerical simulations. Of interest in the present paper are thermal solidification problems involving single or multiple arbitary phases. In order to effectively handle such problems, the finite element method is employed in conjunction with adaptive time stepping approaches to accurately and effectively track the various phase fronts and describe the physics of phase front interactions and thermal behaviour. In conjunction with the enthalpy method which is employed to handle the latent heat release, a fixed‐grid finite element technique and an automatic time stepping approach which uses the norm of the temperature distribution differences between adjacent time step levels to control the error are employed with the scale of the norm being automatically selected. Several numerical examples, including single and multiple phase change problems, are described.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 March 2023

David Tae and Kumar K. Tamma

The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order…

Abstract

Purpose

The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order time accurate, and useful for practical applications, have a significant limitation. They do not account for separable controllable numerical dissipation of the primary variables. Furthermore, they have little or no significant choices of altogether different algorithms that can be integrated in a single analysis to mitigate numerical oscillations that may occur. In lieu of such limitations, under the generalized single-step single-solve (GS4) umbrella, several of the deficiencies are circumvented.

Design/methodology/approach

The GS4 framework encompasses a wide variety of LMS schemes that are all second-order time accurate and offers controllable numerical dissipation. Unlike existing state-of-art, the present framework permits implicit–implicit and implicit–explicit coupling of algorithms via differential algebraic equations (DAE). As further advancement, this study embeds proper orthogonal decomposition (POD) to further reduce model sizes. This study also uses an iterative convergence check in acquiring sufficient snapshot data to adequately capture the physics to prescribed accuracy requirements. Simple linear/nonlinear transient numerical examples are presented to provide proof of concept.

Findings

The present DAE-GS4-POD framework has the flexibility of using different spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency.

Originality/value

The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous DAE-GS4 framework and the improvement of the computational efficiency. The proposed framework/tool kit provides all the needed flexibility, robustness and adaptability for engineering computations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 February 1988

Kumar K. Tamma and Sudhir B. Railkar

The present paper describes the applicability of hybrid transfinite element modelling/analysis formulations for non‐linear heat conduction problems involving phase change. The…

Abstract

The present paper describes the applicability of hybrid transfinite element modelling/analysis formulations for non‐linear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modelling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modelled using enthalpy formulations to enable a physically realistic approximation to be effectively dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modelling/analysis of non‐linear heat conduction problems involving phase change.

Details

Engineering Computations, vol. 5 no. 2
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 May 1999

Kumar K. Tamma, Xiangmin Zhou and Desong Sha

The time‐discretization process of transient equation systems is an important concern in computational heat transfer applications. As such, the present paper describes a formal…

Abstract

The time‐discretization process of transient equation systems is an important concern in computational heat transfer applications. As such, the present paper describes a formal basis towards providing the theoretical concepts, evolution and development, and characterization of a wide class of time discretized operators for transient heat transfer computations. Therein, emanating from a common family tree and explained via a generalized time weighted philosophy, the paper addresses the development and evolution of time integral operators [IO], and leading to integration operators [InO] in time encompassing single‐step integration operators [SSInO], multi‐step integration operators [MSInO], and a class of finite element in time integration operators [FETInO] including the relationships and the resulting consequences. Also depicted are those termed as discrete numerically assigned [DNA] algorithmic markers essentially comprising of both: the weighted time fields, and the corresponding conditions imposed upon the dependent variable approximation, to uniquely characterize a wide class of transient algorithms. Thereby, providing a plausible standardized formal ideology when referring to and/or relating time discretized operators applicable to transient heat transfer computations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 2004

Christianne V.D.R. Anderson and Kumar K. Tamma

We first provide an overview of some predominant theoretical methods currently used for predicting thermal conductivity of thin dielectric films: the equation of radiative…

2789

Abstract

We first provide an overview of some predominant theoretical methods currently used for predicting thermal conductivity of thin dielectric films: the equation of radiative transfer, the temperature‐dependent thermal conductivity theories based on the Callaway model, and the molecular dynamics simulation. This overview also highlights temporal and spatial scale issues by looking at a unified theory that bridges physical issues presented in the Fourier and Cattaneo models. This newly developed unified theory is the so‐called C‐ and F‐processes constitutive model. This model introduces the notion of a new dimensionless heat conduction model number, which is the ratio of the thermal conductivity of the fast heat carrier F‐processes to the total thermal conductivity comprised of both the fast heat carriers F‐processes and the slow heat carriers C‐processes. Illustrative numerical examples for prediction of thermal conductivity in thin films are primarily presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 September 2023

Yazhou Wang, Dehong Luo, Xuelin Zhang, Zhitao Wang, Hui Chen, Xiaobo Zhang, Ningning Xie, Shengwei Mei, Xiaodai Xue, Tong Zhang and Kumar K. Tamma

The purpose of this paper is to design a simple and accurate a-posteriori Lagrangian-based error estimator is developed for the class of backward differentiation formula (BDF…

Abstract

Purpose

The purpose of this paper is to design a simple and accurate a-posteriori Lagrangian-based error estimator is developed for the class of backward differentiation formula (BDF) algorithms with variable time step size, and the adaptive time-stepping in BDF algorithms is demonstrated for efficient time-dependent simulations in fluid flow and heat transfer.

Design/methodology/approach

The Lagrange interpolation polynomial is used to predict the time derivative, and then the accurate primary result is obtained by the Gauss integral, which is applied to evaluate the local error. Not only the generalized formula of the proposed error estimator is presented but also the specific expression for the widely applied BDF1/2/3 is illustrated. Two essential executable MATLAB functions to implement the proposed error estimator are appended for practical applications. Then, the adaptive time-stepping is demonstrated based on the newly proposed error estimator for BDF algorithms.

Findings

The validation tests show that the newly proposed error estimator is accurate such that the effectivity index is always close to unity for both linear and nonlinear problems, and it avoids under/overestimation of the exact local error. The applications for fluid dynamics and coupled fluid flow and heat transfer problems depict the advantage of adaptive time-stepping based on the proposed error estimator for time-dependent simulations.

Originality/value

In contrast to existing error estimators for BDF algorithms, the present work is more accurate for the local error estimation, and it can be readily extended to practical applications in engineering with a few changes to existing codes, contributing to efficient time-dependent simulations in fluid flow and heat transfer.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 25 February 2022

Yazhou Wang, Ningning Xie, Likun Yin, Tong Zhang, Xuelin Zhang, Shengwei Mei, Xiaodai Xue and Kumar Tamma

The purpose of this paper is to describe a novel universal error estimator and the adaptive time-stepping process in the generalized single-step single-solve (GS4-1) computational…

Abstract

Purpose

The purpose of this paper is to describe a novel universal error estimator and the adaptive time-stepping process in the generalized single-step single-solve (GS4-1) computational framework, applied for the fluid dynamics with illustrations to incompressible Navier–Stokes equations.

Design/methodology/approach

The proposed error estimator is universal and versatile that it works for the entire subsets of the GS4-1 framework, encompassing the nondissipative Crank–Nicolson method, the most dissipative backward differential formula and anything in between. It is new and novel that the cumbersome design work of error estimation for specific time integration algorithms can be avoided. Regarding the numerical implementation, the local error estimation has a compact representation that it is determined by the time derivative variables at four successive time levels and only involves vector operations, which is simple for numerical implementation. Additionally, the adaptive time-stepping is further illustrated by the proposed error estimator and is used to solve the benchmark problems of lid-driven cavity and flow past a cylinder.

Findings

The proposed computational procedure is capable of eliminating the nonphysical oscillations in GS4-1(1,1)/Crank–Nicolson method; being CPU-efficient in both dissipative and nondissipative schemes with better solution accuracy; and detecting the complex physics and hence selecting a suitable time step according to the user-defined error threshold.

Originality/value

To the best of the authors’ knowledge, for the first time, this study applies the general purpose GS4-1 family of time integration algorithms for transient simulations of incompressible Navier–Stokes equations in fluid dynamics with constant and adaptive time steps via a novel and universal error estimator. The proposed computational framework is simple for numerical implementation and the time step selection based on the proposed error estimation is efficient, benefiting to the computational expense for transient simulations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 May 1994

N. Brännberg and J. Mackerle

This paper gives a review of the finite element techniques (FE)applied in the area of material processing. The latest trends in metalforming, non‐metal forming and powder…

1437

Abstract

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

Details

Engineering Computations, vol. 11 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 October 2021

Ali Jaber Naeemah and Kuan Yew Wong

The purpose of this paper is (1) to review, analyze and assess the existing literature on lean tools selection studies published from 2005 to 2021; (2) to identify the limitations…

2080

Abstract

Purpose

The purpose of this paper is (1) to review, analyze and assess the existing literature on lean tools selection studies published from 2005 to 2021; (2) to identify the limitations faced by previous studies; and (3) to suggest future works that are necessary to facilitate the selection of lean tools.

Design/methodology/approach

A systematic approach was used in order to identify, collect and select the articles. Several keywords related to the selection of lean tools were used to collect articles from different Scopus indexed journals. Next, the study systematically reviewed and analyzed the selected papers to identify the lean tools' selection method and discussed its features and limitations.

Findings

An analysis of the results showed that previous studies have adopted two types of methods for selecting lean tools. First, there are various traditional methods being used. Second, multi-criteria decision-making (MCDM) methods were commonly used in previous studies, such as the multi-objective decision-making method (MODM), single multi-attribute decision-making (MADM) methods and hybrid (MCDM). Moreover, the study revealed that the lean tools' selection methods in previous studies were based on evaluating the relationship between either lean tools and performance metrics or lean tools and waste, or both.

Research limitations/implications

In terms of its theoretical value, the study is considered as an extension of the previous researches performed on this topic by determining and analyzing the features of the most selection methods of lean tools. Unlike previous review papers, this review had considered discussing and analyzing the characteristics and limitations of these methods. Section 2.2 of this paper reviewed some of the categories of MCDM methods as well as some of the traditional methods used in the selected previous studies. Section 2.1 of this paper explained the concept of lean management and its application benefits. Further, only three sectors were covered by the previous studies in this review paper. This study also provided recommendations for future research. Therefore, it provided researchers with a good conception of how to conduct the studies on lean tools selection. Besides, knowing the methods used in previous studies can help researchers develop new methods to select the best set of lean tools. That is, this study provided and advanced the existing knowledge base for researchers concerning lean tools selection, especially there is limited availability of review papers on this topic. Moreover, the study showed researchers the importance of the relationship between lean tools and indicators or/and performance indicators to determine the appropriate set of lean tools so that the results of future studies will be more realistic and acceptable.

Practical implications

Practically, manufacturers face a significant challenge when selecting proper lean tools. This study may enhance managers, manufacturers and company's knowledge to identify most of the methods used to choose the best set of lean tools and what are the advantages, disadvantages and limitations of these methods as well as the latest studies that have been adopted in this topic. That means this study can direct companies to prioritize the application of lean tools depending on either the manufacturing performance metrics or/and manufacturing wastes so that they avoid incorrect application of lean tools, which will add more non-value added activities to operations. Therefore companies can decrease the time and cost losses and enhancing the quality and efficiency of the performance. Correctly implementing the best set of lean tools in companies will lead in general to correctly applying lean management in corporations. Therefore, these lean tools can boost the economic aspect of companies and society through reducing waste, improving performance indicators, preserving time and cost, achieving quality, efficiency, competitiveness, boosting employee income and improving the gross domestic product. The correct lean tool selection reduces customer complaints and employee stress and improves work conditions, health, safety and labor wellbeing. Besides, the correct lean tools selection improves materials usage, energy usage, water usage and decreases liquid wastes, solid wastes and air emissions. As a result, the right selection of lean tools will have positive effects on both the environment and society. The study may also encourage manufacturers and researchers to adopt studies on lean tools selection in small- and medium-sized companies because the study referred to the importance and participation of these kinds of companies in a large proportion of the economy of developing countries. Further, the study may encourage some countries that have not previously adopted this type of study, academically and industrially to conduct lean tools selection studies.

Social implications

As mentioned previously, the correct lean tool selection reduces customer complaints and employee stress and improves work conditions, health, safety and labor wellbeing. The proper lean tools selection improves materials usage, energy usage, water usage and decreases liquid wastes, solid wastes and air emissions. As a result, the right choice of lean tools will positively affect both the environment and society.

Originality/value

The study expanded the efforts of previous studies concerning lean management features. It provided an accurate review of most lean tools selection studies published from 2005 to 2021 and was not limited to the manufacturing sector. It further identified and briefly described the selection methods concerning lean tools adopted in each paper.

Details

International Journal of Productivity and Performance Management, vol. 72 no. 4
Type: Research Article
ISSN: 1741-0401

Keywords

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