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Article
Publication date: 15 June 2020

Yang Zhang, Wei Liu, Yongkang Lu, Xikang Cheng, Weiqi Luo, Hongtu Di and Fuji Wang

Profile measurement with boundary information plays a vital role in the detection of quality in the assembly of aviation parts. The purpose of this paper is to improve the…

Abstract

Purpose

Profile measurement with boundary information plays a vital role in the detection of quality in the assembly of aviation parts. The purpose of this paper is to improve the evaluation accuracy of the aerodynamic shapes of airplanes, the profiles of large-sized parts need to be measured accurately.

Design/methodology/approach

In this paper, an accurate profile measurement method based on boundary reference points is proposed for the industrial stereo-vision system. Based on the boundary-reference points, the authors established a priori constraint for extracting the boundary of the measured part. Combining with the image features of background and the measured part, an image-edge compensation model is established to extract the boundary of the measured part. The critical point of a laser stripe on the edge of the measured part is extracted corresponding to the boundary constraint. Finally, as per the principle of binocular vision, the profile of the measured part is reconstructed.

Finding

Laboratory experiments validate the measurement accuracy of the proposed method which is 0.33 mm. In the analysis of results between the measured data and the theoretical model, the measuring accuracy of the proposed method was found to be significantly higher than that of the other traditional methods.

Practical implication

An aviation part was measured in the part-assembly shop by the proposed method, which verified the feasibility and effectiveness of this method. The research can realize the measurement of smooth surface boundary which can solve existing profile reconstruction problems for aviation parts.

Originality/value

According to the two-dimensional contour constraint, critical points of the laser strip sequence at the edge of measured part are extracted and the accurate profile reconstruction with the boundary is realized.

Details

Sensor Review, vol. 40 no. 4
Type: Research Article
ISSN: 0260-2288

Keywords

Article
Publication date: 13 July 2021

Shayan Naseri Nia, Faranak Rabiei and M.M. Rashidi

This paper aims to use the Lattice Boltzmann method (LBM) to numerically simulate the natural convection heat transfer of Cu-water nanofluid in an L-shaped enclosure with curved…

Abstract

Purpose

This paper aims to use the Lattice Boltzmann method (LBM) to numerically simulate the natural convection heat transfer of Cu-water nanofluid in an L-shaped enclosure with curved boundaries.

Design/methodology/approach

LBM on three different models of curved L-shape cavity using staircase approach is applied to perform a comparative investigation for the effects of curved boundary on fluid flow and heat transfer. The staircase approximation is a straightforward and efficient approach to simulating curved boundaries in LBM.

Findings

The effect of curved boundary on natural convection in different parameter ranges of Rayleigh number and nanoparticle volume fraction is investigated. The curved L-shape results are also compared to the rectangular L-shape results that were also achieved in this study. The curved boundary LBM simulation is also validated with existing studies, which shows great accuracy in this study. The results show that the top curved boundary in curved L-shape models causes a notable increase in the Nusselt number values.

Originality/value

Based on existing literature, there is a lack of comparative studies which would specifically examine the effects of curved boundaries on natural convection in closed cavities. Particularly, the application of curved boundaries to an L-shape cavity has not been examined. In this study, curved boundaries are applied to the sharp corners of the bending section in the L-shape and the results of the curved L-shape models are compared to the simple rectangular L-shape model. Hence, a comparative evaluation is performed for the effect of curved boundaries on fluid flow in the L-shape enclosure.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 July 2010

Francisco Bernal and Manuel Kindelan

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The…

Abstract

Purpose

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme.

Design/methodology/approach

Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF‐based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.

Findings

The paper shows that the exponential convergence both with increasing resolution and increasing shape parameter, which is typical of the RBF method, is lost in problems containing singularities. The accuracy of the solution can be increased by collocation of the partial differential equation (PDE) at boundary nodes. However, in order to restore the exponential convergence of the RBF method, it is necessary to use special functions which capture the behavior of the solution near the discontinuity.

Practical implications

The paper uses Motz's problem as a prototype for problems described by elliptic partial differential equations with boundary singularities. However, the results obtained in the paper are applicable to a wide range of problems containing boundaries with conditions which change from Dirichlet to Neumann, thus leading to singularities in the first derivatives.

Originality/value

The paper shows that both the global RBF collocation method and the LRBFDQ method, are truly meshless methods which can be very useful for the solution of elliptic problems with boundary singularities. In particular, when complemented with special functions that capture the behavior of the solution near the discontinuity, the method exhibits exponential convergence both with resolution and with shape parameter.

Details

Engineering Computations, vol. 27 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 1996

C. Shu, Y.T. Chew, B.C. Khoo and K.S. Yeo

The global methods of generalized differential quadrature (GDQ) andgeneralized integral quadrature (GIQ) are applied to solve three‐dimensional,incompressible, laminar boundary

Abstract

The global methods of generalized differential quadrature (GDQ) and generalized integral quadrature (GIQ) are applied to solve three‐dimensional, incompressible, laminar boundary layer equations. The streamwise and crosswise velocity components are taken as the dependent variables. The normal velocity is obtained by integrating the continuity equation along the normal direction where the integral is approximated by GIQ approach with high order of accuracy. All the spatial derivatives are discretized by a GDQ scheme. After spatial discretization, the resultant ordinary differential equations are solved by the 4‐stage Runge—Katta scheme. Application of GDQ—GIQ approach to a test problem demonstrated that accurate numerical results can be obtained using just a few grid points.

Details

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

Keywords

Article
Publication date: 5 August 2019

Huifang Li, Mi Zhao, Lihua Wu, Piguang Wang and Xiuli Du

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded…

Abstract

Purpose

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

Design/methodology/approach

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

Findings

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

Originality/value

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

Details

Engineering Computations, vol. 36 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 16 April 2018

Jacek Ptaszny and Marcin Hatłas

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear…

Abstract

Purpose

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time.

Design/methodology/approach

The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered.

Findings

FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver.

Research limitations/implications

The present results are limited to linear elasticity.

Originality/value

This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

Article
Publication date: 19 June 2023

Teng Wen, Xiaoyun Wei, Xuebao Li, Boyuan Cao and Zhibin Zhao

This paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal…

Abstract

Purpose

This paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation.

Design/methodology/approach

Firstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin’s method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given.

Findings

The FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs’ code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs.

Originality/value

The FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 August 2017

Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma and Xiaolin Chang

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial…

Abstract

Purpose

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.

Design/methodology/approach

An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.

Findings

The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..

Originality/value

Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

Details

Engineering Computations, vol. 34 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 May 2016

Rhodri LT Bevan, Etienne Boileau, Raoul van Loon, R.W. Lewis and P Nithiarasu

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not…

Abstract

Purpose

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

Design/methodology/approach

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

Findings

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

Originality/value

A comprehensive comparison between three versions of the CBS method is provided for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 1998

Ch. Provatidis

This paper presents a methodology, based on the fast Fourier transform (FFT), that improves prior established techniques to solve axisymmetric potential problems with…

Abstract

This paper presents a methodology, based on the fast Fourier transform (FFT), that improves prior established techniques to solve axisymmetric potential problems with non‐axisymmetric boundary conditions using the boundary element method (BEM). The proposed methodology is highly effective, especially in cases where a large number of harmonics is required. Furthermore, it is optimised at several levels, reaching the maximum possible efficiency. Special concern is given on its implementation on quadratic elements that are of current practice. The method is applicable to any type of boundary elements as well as to a wider class of static and dynamic axisymmetric boundary value problems.

Details

Engineering Computations, vol. 15 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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