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Article
Publication date: 4 May 2012

Stephen Brill and Eric Smith

The purpose of this paper is to present the analytical solution to the Hermite collocation discretization of a quadratically forced steady‐state convection‐diffusion equation in…

169

Abstract

Purpose

The purpose of this paper is to present the analytical solution to the Hermite collocation discretization of a quadratically forced steady‐state convection‐diffusion equation in one spatial dimension with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. To improve the accuracy of the method “upstream weighting” of the convective term is used in an optimal way. The authors also provide a method to determine where the forcing function should be optimally sampled. Computational examples are given, which support and illustrate the theory of the optimal sampling of the convective and forcing term.

Design/methodology/approach

The authors: extend previously published results (which dealt only with the case of linear forcing) to the case of quadratic forcing; prove the theorem that governs the quadratic case; and then illustrate the results of the theorem using computational examples.

Findings

The algorithm developed for the quadratic case dramatically decreases the error (i.e. the difference between the continuous and numerical solutions).

Research limitations/implications

Because the methodology successfully extends the linear case to the quadratic case, it is hoped that the method can, indeed, be extended further to more general cases. It is true, however, that the level of complexity rose significantly from the linear case to the quadratic case.

Practical implications

Hermite collocation can be used in an optimal way to solve differential equations, especially convection‐diffusion equations.

Originality/value

Since convection‐dominated convection‐diffusion equations are difficult to solve numerically, the results in this paper make a valuable contribution to research in this field.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 August 2009

Karen L. Ricciardi and Stephen H. Brill

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be…

282

Abstract

Purpose

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be used to model the transport of contaminants dissolved in groundwater). This accuracy is dependent upon sufficient refinement of the finite‐element mesh as well as applying upstream or downstream weighting to the convective term through the determination of collocation locations which meet specified constraints. Owing to an increase in computational intensity of the application of the method of collocation associated with increases in the mesh refinement, minimal mesh refinement is sought. Very often this optimization problem is the one where the feasible region is not connected and as such requires a specialized optimization search technique. This paper aims to focus on this method.

Design/methodology/approach

An original hybrid method that utilizes a specialized adaptive genetic algorithm followed by a hill‐climbing approach is used to search for the optimal mesh refinement for a number of models differentiated by their velocity fields. The adaptive genetic algorithm is used to determine a mesh refinement that is close to a locally optimal mesh refinement. Following the adaptive genetic algorithm, a hill‐climbing approach is used to determine a local optimal feasible mesh refinement.

Findings

In all cases the optimal mesh refinements determined with this hybrid method are equally optimal to, or a significant improvement over, mesh refinements determined through direct search methods.

Research limitations

Further extensions of this work could include the application of the mesh refinement technique presented in this paper to non‐steady‐state problems with time‐dependent coefficients with multi‐dimensional velocity fields.

Originality/value

The present work applies an original hybrid optimization technique to obtain highly accurate solutions using the method of Hermite collocation with minimal mesh refinement.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 October 1984

Energy efficiency information centre. With major support from the Department of Energy's Energy Efficiency Office, the Building Centre in London's Store Street is to house an…

121

Abstract

Energy efficiency information centre. With major support from the Department of Energy's Energy Efficiency Office, the Building Centre in London's Store Street is to house an energy efficiency centre—a joint venture between the office and trade associations and fuel industries. To open in mid‐October, it will take the form of a regularly updated exhibition area with information officers to answer day‐to‐day queries and professional consultants available, by appointment, to deal with specific technical problems.

Details

Facilities, vol. 2 no. 10
Type: Research Article
ISSN: 0263-2772

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Article
Publication date: 1 July 1985

Some controversy has been stirred up by the conclusion, reached in the BOSTI report on office design and productivity, that design has a calculable dollar premium. In response to…

67

Abstract

Some controversy has been stirred up by the conclusion, reached in the BOSTI report on office design and productivity, that design has a calculable dollar premium. In response to Peter Ellis's detailed, point by point analysis of the report (Vol 3/No 1/January) the joint authors have made an equally detailed rebuttal.

Details

Facilities, vol. 3 no. 7
Type: Research Article
ISSN: 0263-2772

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Article
Publication date: 1 December 1994

Marilyn P. Rowan and Phillip C. Wright

Ergonomics refers to the complex relationship between workers and theirwork that permeates every aspect of the workplace. Originally definedin 1717 by Bernadino Ramazinni, an…

3532

Abstract

Ergonomics refers to the complex relationship between workers and their work that permeates every aspect of the workplace. Originally defined in 1717 by Bernadino Ramazinni, an Italian physician credited as the founder of occupational medicine, it is only recently that ergonomics has attracted widespread attention. This article will illustrate that the increasing interest in ergonomics is warranted and that appropriate ergonomic management is a process that will have a significant, positive effect on a company′s profits through cost reduction, quality improvement, performance improvement and productivity enhancement. Derived from the Greek words ergo and nomos meaning “work” and “natural laws”, ergonomics literally means the laws of work.

Details

Work Study, vol. 43 no. 8
Type: Research Article
ISSN: 0043-8022

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Available. Content available
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Publication date: 8 September 2022

Stephen Turner

Free Access. Free Access

Abstract

Details

Mad Hazard
Type: Book
ISBN: 978-1-80382-670-7

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Article
Publication date: 9 September 2014

Peter Wellburn

340

Abstract

Details

Reference Reviews, vol. 28 no. 7
Type: Research Article
ISSN: 0950-4125

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Article
Publication date: 1 May 2003

Stephen V. Pomes

401

Abstract

Details

Reference Reviews, vol. 17 no. 5
Type: Research Article
ISSN: 0950-4125

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Abstract

Details

Inside Major East Asian Library Collections in North America, Volume 2
Type: Book
ISBN: 978-1-80455-140-0

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Abstract

Details

Reference Reviews, vol. 21 no. 7
Type: Research Article
ISSN: 0950-4125

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