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  • Open Access

    ARTICLE

    FDMFS for Diffusion Equation with Unsteady Forcing Function

    S.P. Hu1, D.L. Young2, C.M. Fan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 1-20, 2008, DOI:10.3970/cmes.2008.024.001

    Abstract In this paper, a novel numerical scheme called (FDMFS), which combines the finite difference method (FDM) and the method of fundamental solutions (MFS), is proposed to simulate the nonhomogeneous diffusion problem with an unsteady forcing function. Most meshless methods are confined to the investigations of nonhomogeneous diffusion equations with steady forcing functions due to the difficulty to find an unsteady particular solution. Therefore, we proposed a FDM with Cartesian grid to handle the unsteady nonhomogeneous term of the equations. The numerical solution in FDMFS is decomposed into a particular solution and a homogeneous solution. The particular solution is constructed using… More >

  • Open Access

    ARTICLE

    A Smoothed Four-Node Piezoelectric Element for Analysis of Two-Dimensional Smart Structures

    H. Nguyen-Van1, N. Mai-Duy2, T. Tran-Cong3

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

    Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated.… More >

  • Open Access

    ARTICLE

    Improving Volume Element Methods by Meshless Radial Basis Function Techniques

    P. Orsini1, H. Power1,2, H. Morvan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 187-208, 2008, DOI:10.3970/cmes.2008.023.187

    Abstract In this work, we present a modified Control Volume (CV) method that uses a Radial Basis Function (RBF) interpolation to improve the prediction of the flux accuracy at the faces of the CV. The method proposed differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. In addition, it is required… More >

  • Open Access

    ARTICLE

    Modeling and Bending Vibration of the Blade of a Horizontal-Axis Wind Power Turbine

    Shueei-Muh Lin1, Sen-Yung Lee2, Yu-Sheng Lin3

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 175-186, 2008, DOI:10.3970/cmes.2008.023.175

    Abstract The blade of a horizontal-axis wind power turbine is modeled as a rotating beam with pre-cone angles and setting angles. Based on the Bernoulli-Euler beam theory, without considering the axial extension deformation and the Coriolis forces effect, the governing differential equations for the bending vibration of the beam are derived. It is pointed out that if the geometric and the material properties of the beam are in polynomial forms, then the exact solution for the system can be obtained. Based on the frequency relations as revealed, without tedious numerical analysis, one can reach many general qualitative conclusions between the natural… More >

  • Open Access

    ARTICLE

    Boundary Element Method for an Inverse Problem in Magnetic Resonance Imaging Gradient Coils

    Liviu Marin1, Henry Power1, Richard W. Bowtell2, Clemente Cobos Sanchez2, Adib A. Becker1, Paul Glover2,Arthur Jones1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 149-174, 2008, DOI:10.3970/cmes.2008.023.149

    Abstract We investigate the reconstruction of a divergence-free surface current distribution from knowledge of the magnetic flux density in a prescribed region of interest in the framework of static electromagnetism. This inverse problem is motivated by the design of gradient coils for use in magnetic resonance imaging (MRI) and is formulated using its corresponding integral representation according to potential theory. A novel boundary element method (BEM) which employs linear interpolation on quadratic surfaces and also satisfies the continuity equation for the current density, i.e. a divergence-free BEM, is presented. Since the discretised BEM system is ill-posed and hence the associated least-squares… More >

  • Open Access

    ARTICLE

    A Hybrid Multi-Region BEM / LBIE-RBF Velocity-Vorticity Scheme for the Two-Dimensional Navier-Stokes Equations

    E.J. Sellountos1, A. Sequeira1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 127-148, 2008, DOI:10.3970/cmes.2008.023.127

    Abstract In this work a hybrid velocity-vorticity scheme for the solution of the 2D Navier-Stokes equations is presented. The multi-region Local Boundary Integral Equation (LBIE) combined with Radial Basis Functions (RBF) interpolation is used for the solution of the kinematics and the multi-region BEM for the solution of the transport kinetics. The final system of equations is in band form for both methods. The issue of RBF discontinuities is resolved by constructing the RBF matrix locally in every region. The kinematics integral equation is used in three different forms, for coupling the velocity field on the boundary, on interior points and… More >

  • Open Access

    ARTICLE

    Property Predictions for Packed Columns Using Monte Carlo and Discrete Element Digital Packing Algorithms

    C. Xu1, X. Jia2, R. A. Williams2, E. H. Stitt3, M. Nijemeisland3, S. El-Bachir4, A. J. Sederman4, L. F. Gladden4

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 117-126, 2008, DOI:10.3970/cmes.2008.023.117

    Abstract Existing theories and computer models for packed columns are either incapable of handling complex pellet shapes or based on over-simplified packing geometry. A digital packing algorithm, namely DigiPac, has recently been developed to fill the gap. It is capable of packing of particles of any shapes and sizes in a container of arbitrary geometry, and is a first step towards a practical computational tool for reliable predictions of packed column properties based on the actual pellet shapes. DigiPac can operate in two modes: a Monte Carlo mode in which particles undergo directional diffusive motions; and a Discrete Element mode where… More >

  • Open Access

    ARTICLE

    The Stochastic α Method: A Numerical Method for Simulation of Noisy Second Order Dynamical Systems

    Nagalinga Rajan, Soumyendu Raha1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 91-116, 2008, DOI:10.3970/cmes.2008.023.091

    Abstract The article describes a numerical method for time domain integration of noisy dynamical systems originating from engineering applications. The models are second order stochastic differential equations (SDE). The stochastic process forcing the dynamics is treated mainly as multiplicative noise involving a Wiener Process in the Itô sense. The developed numerical integration method is a drift implicit strong order 2.0 method. The method has user-selectable numerical dissipation properties that can be useful in dealing with both multiplicative noise and stiffness in a computationally efficient way. A generalized analysis of the method including the multiplicative noise is presented. Strong order convergence, user-selectable… More >

  • Open Access

    ARTICLE

    A New Meshless Interpolation Scheme for MLPG_R Method

    Q.W. Ma1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 75-90, 2008, DOI:10.3970/cmes.2008.023.075

    Abstract In the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, one needs a meshless interpolation scheme for an unknown function to discretise the governing equation. The MLS (moving least square) method has been used for this purpose so far. The MLS method requires inverse of matrix or solution of a linear algebraic system and so is quite time-consuming. In this paper, a new scheme, called simplified finite difference interpolation (SFDI), is devised. This scheme is generally as accurate as the MLS method but does not need matrix inverse and consume less CPU time to evaluate. Although this scheme… More >

  • Open Access

    ARTICLE

    Consolidation of a Soft Clay Composite: Experimental Results and Computational Estimates

    A.P.S. Selvadurai1, H. Ghiabi2

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.1, pp. 53-74, 2008, DOI:10.3970/cmes.2008.023.053

    Abstract This paper deals with the problem of the consolidation of a composite consisting of alternate layers of soft clay and a granular material. A series of experiments were conducted on components to develop the constitutive models that can be implemented in a computational approach. The constitutive response of the soft clay is represented by a poro-elasto-plastic Cam clay-based model and the granular medium by an elasto-plastic model with a Drucker-Prager type failure criterion and a non-associated flow rule. The computational poro-elasto-plastic model is used to calibrate the experimental results derived from the one-dimensional tests and to establish the influence of… More >

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