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…
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.
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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…
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.
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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…
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.
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…
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.
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…
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.