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  • Open Access

    ARTICLE

    Error Bounds forDiscrete Geometric Approach

    Lorenzo Codecasa1, Francesco Trevisan2

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 155-180, 2010, DOI:10.3970/cmes.2010.059.155

    Abstract Electromagnetic problems spatially discretized by the so called Discrete Geometric Approach are considered, where Discrete Counterparts of Constitutive Relations are discretized within an Energetic Approach. Pairs of oriented dual grids are considered in which the primal grid is composed of (oblique) parallelepipeds, (oblique) triangular prisms and tetrahedra and the dual grid is obtained according to the barycentric subdivision. The focus of the work is the evaluation of the constants bounding the approximation error of the electromagnetic field; the novelty is that such constants will be expressed in terms of the geometrical details of oriented dual grids. A numerical analysis will… More >

  • Open Access

    ARTICLE

    A Comparative Study of Global and Local Meshless Methods for Diffusion-Reaction Equation

    Guangming Yao1, Siraj-ul-Islam2, Božidar Šarler2

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 127-154, 2010, DOI:10.3970/cmes.2010.059.127

    Abstract This paper focuses on the comparative study of global and local meshless methods based on collocation with radial basis functions for solving two dimensional initial boundary value diffusion-reaction problem with Dirichlet and Neumann boundary conditions. A similar study was performed for the boundary value problem with Laplace equation by Lee, Liu, and Fan (2003). In both global and local methods discussed, the time discretization is performed in explicit and implicit way and the multiquadric radial basis functions (RBFs) are used to interpolate diffusion-reaction variable and its spatial derivatives. Five and nine nodded sub-domains are used in the local support of… More >

  • Open Access

    ARTICLE

    Analytic Closed Solution for the Heat Conduction with Time Dependent Heat Convection Coefficient at One Boundary

    Han Taw Chen1, Shao Lun Sun1, Hui Chen Huang1, Sen Yung Lee1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 107-126, 2010, DOI:10.3970/cmes.2010.059.107

    Abstract A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for the one term approximation solution… More >

  • Open Access

    ARTICLE

    A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems

    Peter Lucas1, Alexander H. van Zuijlen1, Hester Bijl1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 79-106, 2010, DOI:10.3970/cmes.2010.059.079

    Abstract Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.
    In previous work [Lucas, P.,Bijl, H., and Zuijlen, A.H. van(2010)], we have shown that a Jacobian-free Newton-Krylov (JFNK) algorithm, preconditioned with an approximate factorization of the Jacobian which approximately matches the target residual operator, enables a speed up of a factor of 10 compared to nonlinear multigrid (NMG) for two-dimensional, large Reynolds number, unsteady flow computations. Furthermore, in [Lucas, P., Zuijlen, A.H. van, and Bijl, H. (2010)] we show that this algorithm also greatly outperforms NMG for parameter… More >

  • Open Access

    ARTICLE

    A Fractional Order HIV Internal Viral Dynamics Model

    Caibin Zeng1, Qigui Yang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 65-78, 2010, DOI:10.3970/cmes.2010.059.065

    Abstract In this paper, a fractional order model is established to describe HIV internal viral dynamics involving HAART effect. First, the model is proved to possess non-negative solutions as desired in any population dynamics. Then, a detailed analysis is carried out to study the stability of equilibrium points. Numerical simulations are presented to illustrate the stability analysis. More >

  • Open Access

    ARTICLE

    Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number

    G.C. Bourantas1, E.D. Skouras2,3, V.C. Loukopoulos4, G.C. Nikiforidis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 31-64, 2010, DOI:10.3970/cmes.2010.059.031

    Abstract A meshfree point collocation method has been developed for the velocity-vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc -tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through two representative, well-known, and… More >

  • Open Access

    ARTICLE

    Multi-field Coupling of Particulate Systems

    K. Han1, Y. T. Feng1, D. R. J. Owen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 1-30, 2010, DOI:10.3970/cmes.2010.059.001

    Abstract A computational framework is established for effective modelling of fluid-thermal-particle interactions. The numerical procedures comprise the Discrete Element Method for simulating particle dynamics; the Lattice Boltzmann Method for modelling the mass and velocity field of the fluid flow; and the Discrete Thermal Element Method and the Thermal Lattice Boltzmann Method for solving the temperature field. The coupling of the three fields is realised through hydrodynamic interaction force terms. Selected numerical examples are provided to illustrate the applicability of the proposed approach. More >

  • Open Access

    ARTICLE

    Galerkin Boundary Integral Analysis forthe 3D Helmholtz Equation

    M. R. Swager1, L. J. Gray2, S. Nintcheu Fata2

    CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 297-312, 2010, DOI:10.3970/cmes.2010.058.297

    Abstract A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential… More >

  • Open Access

    ARTICLE

    On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber

    A. Frangi1, M. Bonnet2

    CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 271-296, 2010, DOI:10.3970/cmes.2010.058.271

    Abstract This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number N of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For β ≥ 1 it is observed that the… More >

  • Open Access

    ARTICLE

    Analysis of a Crack in a Thin Adhesive Layer between Orthotropic Materials: An Application to Composite Interlaminar Fracture Toughness Test

    L. Távara1, V. Manticˇ 1, E. Graciani1, J. Cañas1, F. París1

    CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 247-270, 2010, DOI:10.3970/cmes.2010.058.247

    Abstract The problem of a crack in a thin adhesive layer is considered. The adherents may have orthotropic elastic behavior which allows composite laminates to be modeled. In the present work a linear elastic-brittle constitutive law of the thin adhesive layer, called weak interface model, is adopted, allowing an easy modeling of crack propagation along it. In this law, the normal and tangential stresses across the undamaged interface are proportional to the relative normal and tangential displacements, respectively. Interface crack propagation is modeled by successive breaking of the springs used to discretize the weak interface. An important feature of the BEM… More >

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