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  • Open Access


    Performance of Multiquadric Collocation Method in Solving Lid-driven Cavity Flow Problem with Low Reynolds Number

    S. Chantasiriwan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 137-146, 2006, DOI:10.3970/cmes.2006.015.137

    Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity formulation and the velocity-vorticity formulation.… More >

  • Open Access


    Local Defect Correction for the Boundary Element Method

    G. Kakuba1, R.M.M. Mattheij2, M.J.H. Anthonissen3

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 127-136, 2006, DOI:10.3970/cmes.2006.015.127

    Abstract This paper presents an efficient way to implement the Boundary Element Method (BEM) to capture high activity regions in a boundary value problem. In boundary regions where accuracy is critical, like in adaptive surface meshes, the method of choice is Local Defect Correction (LDC). We formulate the method and demonstrate its applicability and reliability by means of an example. Numerical results show that LDC and BEM together provide accurate solutions with less computational requirements given that BEM systems usually consist of dense matrices. More >

  • Open Access


    Green Functions for a Continuously Non-homogeneous Saturated Media

    Sarang Seyrafian1, Behrouz Gatmiri2, Asadollah Noorzad3

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 115-126, 2006, DOI:10.3970/cmes.2006.015.115

    Abstract An analytical solution is presented for the response of a non-homogeneous saturated poroelastic half-space under the action of a time-harmonic vertical point load on its surface. The shear modulus is assumed to increase continuously with depth and also the media is considered to obey Biot's poroelastic theory. The system of governing partial differential equations, based on the mentioned assumptions, is converted to ordinary differential equations' system by means of Hankel integral transforms. Then the system of equations is solved by use of generalized power series(Frobenius method) and the expressions for displacements in the interior of the media or in the… More >

  • Open Access


    The Detection of Super-elliptical Inclusions in Infrared Computerised Axial Tomography

    N.S.Mera1, L. Elliott2, D.B.Ingham2

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 107-114, 2006, DOI:10.3970/cmes.2006.015.107

    Abstract The purpose of this study is to investigate the efficiency, accuracy and rate of convergence of an evolutionary algorithm for detecting inclusions parametrised by superellipses in non-destructive evaluation and testing. The inverse problem investigated consists of identifying the geometry of discontinuities in a conductive material from Cauchy data measurements taken on the boundary. Temperature and heat flux are measured on the outside boundary of the domain and the position and the size of a super-elliptical inclusion are determined by minimising an objective functional using an evolution strategy. The super-elliptical form allows the parametric model to characterise a variety of shapes… More >

  • Open Access


    Topology Optimization of 2D Potential Problems Using Boundary Elements

    Adrián P. Cisilino1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 99-106, 2006, DOI:10.3970/cmes.2006.015.099

    Abstract Topological Optimization provides a powerful framework to obtain the optimal domain topology for several engineering problems. The Topological Derivative is a function which characterizes the sensitivity of a given problem to the change of its topology, like opening a small hole in a continuum or changing the connectivity of rods in a truss.
    A numerical approach for the topological optimization of 2D potential problems using Boundary Elements is presented in this work. The formulation of the problem is based on recent results which allow computing the topological derivative from potential and flux results. The Boundary Element analysis is done… More >

  • Open Access


    Application of Boundary Element Method to Modelling of Added Mass and Its Effect on Hydrodynamic Forces

    Paola Gardano1, Peter Dabnichki1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 87-98, 2006, DOI:10.3970/cmes.2006.015.087

    Abstract The work presents a numerical simulation of hydrodynamic forces generated in front crawl swimming. The three dimensional Laplace's equation is used for the analysis of the flow around a moving body in an infinite domain and considers the effect of the added mass and the acceleration on the hydrodynamic forces (Drag and Lift) generated by the interaction between the flow and the body at different geometric configurations of the arm -- variable elbow angle. Boundary Element Method (BEM) was used to obtain the solution of the three dimensional equation numerically. The aim of the work was two-fold:
    1) to… More >

  • Open Access


    Efficient Shooting Methods for the Second-Order Ordinary Differential Equations

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 69-86, 2006, DOI:10.3970/cmes.2006.015.069

    Abstract In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at t=0 and t=T in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(u0,uT) and the establishment of a mid-point Lie group element G(r). Then, by imposing G(u0,uT) = G(r) we can search the missing initial conditions through an iterative solution of the weighting factor r ∈ (0,1). Numerical examples were examined to convince that the new approach… More >

  • Open Access


    SPH in a Total Lagrangian Formalism

    Rade Vignjevic1, Juan R. Reveles1, James Campbell1

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 181-198, 2006, DOI:10.3970/cmes.2006.014.181

    Abstract To correct some of the main shortcomings of conventional SPH, a version of this method based on the Total Lagrangian formalism, T. Rabczuk, T. Belytschko and S. Xiao (2004), is developed. The resulting scheme removes the spatial discretisation instability inherent in conventional SPH, J. Monaghan (1992).
    The Total Lagrangian framework is combined with the mixed correction which ensures linear completeness and compliance with the patch test, R. Vignjevic, J. Campbell, L. Libersky (2000). The mixed correction utilizes Shepard Functions in combination with a correction to derivative approximations.
    Incompleteness of the kernel support combined with the lack of consistency… More >

  • Open Access


    The Application of a Hybrid Inverse Boundary Element Problem Engine for the Solution of Potential Problems

    S. Noroozi1, P. Sewell1, J. Vinney1

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 171-180, 2006, DOI:10.3970/cmes.2006.014.171

    Abstract A method that combines a modified back propagation Artificial Neural Network (ANN) and Boundary Element Analysis (BEA) was introduced and discussed in the author's previous papers. This paper discusses the development of an automated inverse boundary element problem engine. This inverse problem engine can be applied to both potential and elastostatic problems.
    In this study, BEA solutions of a two-dimensional potential problem is utilised to test the system and to train a back propagation Artificial Neural Network (ANN). Once training is completed and the transfer function is created, the solution to any subsequent or new problems can be obtained… More >

  • Open Access


    On the NGF Procedure for LBIE Elastostatic Fracture Mechanics

    L.S. Miers1, J.C.F. Telles2

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 161-170, 2006, DOI:10.3970/cmes.2006.014.161

    Abstract This work aims at extending the concept of the Numerical Green's Function (NGF), well known from boundary element applications to fracture mechanics, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals over the crack boundary and is introduced only for source points whose support touches or contains the crack. The results obtained with the coupling of NGF-LBIE in previous potential discontinuity Laplace's equation problems and the authors' experience in NGF-BEM fracture mechanics were the motivation for this development. More >

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