Search results

1 – 10 of 101
To view the access options for this content please click here
Article
Publication date: 1 August 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

Keywords

To view the access options for this content please click here
Article
Publication date: 1 January 2005

S. D'Heedene, K. Amaratunga and J. Castrillón‐Candás

This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.

Abstract

Purpose

This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.

Design/methodology/approach

Second‐generation wavelet construction gives rise to a powerful generalization of the traditional hierarchical basis (HB) finite element method (FEM). A framework based on piecewise polynomial Lagrangian multiwavelets is used to generate customized multiresolution bases that have not only HB properties but also additional qualities.

Findings

For the 1D Poisson problem, we propose – for any given order of approximation – a compact closed‐form wavelet basis that block‐diagonalizes the stiffness matrix. With this wavelet choice, all coupling between the coarse scale and detail scales in the matrix is eliminated. In contrast, traditional higher‐order (n>1) HB do not exhibit this property. We also achieve full scale‐decoupling for the 2D Poisson problem on an irregular mesh. No traditional HB has this quality in 2D.

Research limitations/implications

Similar techniques may be applied to scale‐decouple the multiresolution finite element (FE) matrices associated with more general elliptic PDEs.

Practical implications

By decoupling scales in the FE matrix, the wavelet formulation lends itself particularly well to adaptive refinement schemes.

Originality/value

The paper explains second‐generation wavelet construction in a Lagrangian FE context. For 1D higher‐order and 2D first‐order bases, we propose a particular choice of wavelet, customized to the Poisson problem. The approach generalizes to other elliptic PDE problems.

Details

Engineering Computations, vol. 22 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

To view the access options for this content please click here
Article
Publication date: 8 June 2012

Syed Tauseef Mohyud‐Din, Elham Negahdary and Muhammad Usman

The purpose of this paper is to present a numerical solution of a family of generalized fifth‐order Korteweg‐de Vries equations using a meshless method of lines. This…

Abstract

Purpose

The purpose of this paper is to present a numerical solution of a family of generalized fifth‐order Korteweg‐de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge‐Kutta method as a time integrator and exhibits high accuracy as seen from the comparison with the exact solutions.

Design/methodology/approach

The study uses a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge‐Kutta method as a time integrator.

Findings

The paper reveals that this method exhibits high accuracy as seen from the comparison with the exact solutions.

Originality/value

This method is efficient method as it is easy to implement for the numerical solutions of PDEs.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 20 February 2007

N. Mai‐Duy and R.I. Tanner

To present a new collocation method for numerically solving partial differential equations (PDEs) in rectangular domains.

Abstract

Purpose

To present a new collocation method for numerically solving partial differential equations (PDEs) in rectangular domains.

Design/methodology/approach

The proposed method is based on a Cartesian grid and a 1D integrated‐radial‐basis‐function scheme. The employment of integration to construct the RBF approximations representing the field variables facilitates a fast convergence rate, while the use of a 1D interpolation scheme leads to considerable economy in forming the system matrix and improvement in the condition number of RBF matrices over a 2D interpolation scheme.

Findings

The proposed method is verified by considering several test problems governed by second‐ and fourth‐order PDEs; very accurate solutions are achieved using relatively coarse grids.

Research limitations/implications

Only 1D and 2D formulations are presented, but we believe that extension to 3D problems can be carried out straightforwardly. Further, development is needed for the case of non‐rectangular domains.

Originality/value

The contribution of this paper is a new effective collocation formulation based on RBFs for solving PDEs.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 17 June 2019

Muhammad Raees Ul Haq, Hang Xu and Liang Zhao

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in…

Abstract

Purpose

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in microchannel induced by the pressure in the presence of interfacial electrokinetic effects.

Design/methodology/approach

For the numerical study, the authors implemented traditional FDM approach, and for the regularity results they used the classical energy estimates. The interfacial electrokinetic effects result in an additional source term in classical momentum equation, hence affecting the characteristics of the flow and heat transfer. The sinusoidal temperature variation is assumed on side walls.

Findings

The results were obtained for various combinations of physical parameters appearing in the governing equations. This study concludes that in the presence of electric double layer, the average heat transfer rate reduces along with larger values of Reynolds number. It is observed that the heat transfer increases with the increase in amplitude ratio and phase deviation. The flow behavior and heat transfer rate inside the microchannel are also strongly affected by the presence of κ (kappa).

Originality/value

To the best of the authors’ knowledge, the problem of heat transfer through microchannel in combination with sinusoidal temperature variation at boundary with electric double layer effects has not been considered previously. Hence, this paper focuses on the influence of the sinusoidal boundary temperature distributions on both sidewalls of a rectangular microchannel through parallel plates with electrokinetic effects on the pressure-driven laminar flow. In addition, a detailed mathematical analysis is also to be carried out to verify the regularity of this model with the proposed boundary conditions. The study used the classical energy method to get the regularity results.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 1 May 2001

Eduardo N. Dvorkin

Engineers have developed robust and efficient incompressible finite element formulations using tools such as the Patch Test and the counting of constraints/variables, the…

Abstract

Engineers have developed robust and efficient incompressible finite element formulations using tools such as the Patch Test and the counting of constraints/variables, the first one aimed at the development of consistent elements and the second one aimed at the development of non‐locking and stable elements. The mentioned tools are rooted in the physics of the continuum mechanics problem. Mathematicians, on the other side, developed complex and powerful tools to examine the convergence of finite element formulations, such as the inf‐sup condition, these methods are based on the properties of the elliptical PDEs that constitute the mathematical model of the continuum mechanics problem. In this paper we intend to understand the inf‐sup condition from an engineering perspective, so as to be able to incorporate it into the package of tools used in the development of finite element formulations.

Details

Engineering Computations, vol. 18 no. 3/4
Type: Research Article
ISSN: 0264-4401

Keywords

To view the access options for this content please click here
Article
Publication date: 1 March 2001

Bassam A/K Abu‐Hijleh

The problem of laminar cross‐flow forced convection heat transfer from a horizontal cylinder covered with an orthotropic porous layer was investigated numerically. The…

Abstract

The problem of laminar cross‐flow forced convection heat transfer from a horizontal cylinder covered with an orthotropic porous layer was investigated numerically. The effects of porous layer thickness, radial resistance, tangential resistance, and incoming flow Reynolds number on the average Nusselt number were studied in detail. There was up to 40 per cent reduction in the average Nusselt number at high values of Reynolds number. The tangential resistance effect on the Nusselt number was dominant over that of the radial resistance. The effectiveness of the porous layer increased at high values of porous layer thickness as well as at high values of Reynolds number.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 1 April 2005

Bassam A/K and Abu‐Hijleh

The aim of this work is to determine the optimal number and location of the fin(s) for maximum laminar forced convection heat transfer from a cylinder with multiple high…

Abstract

Purpose

The aim of this work is to determine the optimal number and location of the fin(s) for maximum laminar forced convection heat transfer from a cylinder with multiple high conductivity radial fins on its outer surface in cross‐flow, i.e. Nusselt number, over a range of Reynolds numbers.

Design/methodology/approach

The effect of several combinations of number of fins, fin height, and fin(s) tangential location on the average Nusselt number was studied over the range of Reynolds numbers (5‐150). The problem was investigated numerically using finite difference method over a stretched grid. The optimal number and placement of the fins, for maximum Nusselt number, was determined for several combinations of Reynolds number and fin height. The percentage improvement in heat transfer per fin(s) unit length, i.e. cost‐efficiency, was also studied.

Findings

The results indicate that the fin(s) combination with the highest normalised Nusselt number is not necessarily the combination that results in the highest fin cost‐efficiency.

Originality/value

The results of the study can be used to design highly efficient cross‐flow forced convection heat transfer configurations from a horizontal cylinder with minimum cost.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 10 April 2007

M. de Magistris, M. Morozov, G. Rubinacci, A. Tamburrino and S. Ventre

The paper aims to apply an innovative inversion method to the problem of imaging (location, direction and size) of concrete rebars by means of eddy current measurements.

Abstract

Purpose

The paper aims to apply an innovative inversion method to the problem of imaging (location, direction and size) of concrete rebars by means of eddy current measurements.

Design/methodology/approach

An accurate numerical model of the probe‐rebar interaction, including eddy currents and skin effect, is considered. The inverse problem is approached with a very efficient inversion procedure previously introduced in a different context.

Findings

A critical analysis of the issues to be considered for the quantitative imaging of rebars is given, and the possibility of relevant simplifications in the numerical model outlined, allowing the development of an accurate and computationally efficient method.

Originality/value

The proposed formulation is applied for the first time to the problem of rebars imaging. Experimental tests have been carried out to validate the numerical model and its underlying hypothesis.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 26 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

To view the access options for this content please click here
Article
Publication date: 1 June 1996

M.B. Davis and G.F. Carey

Develops a finite element analysis and solution strategy for the augmented drift‐diffusion equations in semiconductors device theory using a multilevel scheme. Decouples…

Abstract

Develops a finite element analysis and solution strategy for the augmented drift‐diffusion equations in semiconductors device theory using a multilevel scheme. Decouples the drift‐diffusion equations using Gummel iteration with incremental continuation in the applied voltage. Includes augmentation of the carrier mobility to address the issue of non‐local electric field effects (velocity overshoot) within the framework of the drift‐diffusion formulation. Gives comparison results with hydrodynamic and Monte Carlo models and sensitivity studies with respect to the augmentation parameter. Discretizes the equations with a special finite element method using bases of variable polynomial degree. Accomplishes solution of the resulting linear systems with a multilevel method using the basis degree as the grid level. Presents performance results and comparison studies with direct elimination.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 15 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

1 – 10 of 101