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  • Open Access

    ARTICLE

    A Thermal Lattice Boltzmann Model for Flows with Viscous Heat Dissipation

    Hao-Chueh Mai1, Kuen-Hau Lin1, Cheng-Hsiu Yang1, Chao-An Lin1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 45-62, 2010, DOI:10.3970/cmes.2010.061.045

    Abstract A thermal BGK lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the temperature is solved by a separate thermal distribution function, where the equilibrium distribution function is similar to its hydrodynamic counterpart, except that the leading quantity is temperature. The viscous dissipation rate is obtained by computing the second-order moments of non-equilibrium distribution function, which avoids the discretization of the complex gradient term, and can be easily implemented. The proposed thermal lattice Boltzmann model is scrutinized by computing two-dimensional thermal Poiseuille flow, thermal Couette flow, natural convection in a square cavity, and three-dimensional thermal… More >

  • Open Access

    ARTICLE

    An H-Adaptive Finite Element Method for Turbulent Heat Transfer

    David B. Carrington1, Xiuling Wang2, Darrell W. Pepper3

    CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 23-44, 2010, DOI:10.3970/cmes.2010.061.023

    Abstract A two-equation turbulence closure model (k-ω) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement… More >

  • Open Access

    ARTICLE

    Application of Energy Finite Element Method to High-frequency Structural-acoustic Coupling of an Aircraft Cabin with Truncated Conical Shape

    M. X. Xie1, H. L. Chen1, J. H. Wu1, F. G. Sun1

    CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.061.001

    Abstract Energy finite element method (EFEM) is a new method to solve high-frequency structural-acoustic coupling problems, but its use has been limited to solving simple structures such as rods, beams, plates and combined structures. In this paper, the high-frequency structural-acoustic coupling characteristics of an aircraft cabin are simulated by regarding the shell as a number of flat shell elements connected with a certain angle in EFEM. Two tests validated the method employed in this paper. First, the structural response analysis of a cylinder was calculated in two ways: dividing the shell by axis-symmetric shells after deriving the governing equation of axis-symmetric… More >

  • Open Access

    ARTICLE

    Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems

    Chein-Shan Liu1, Hong-Ki Hong1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279

    Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications of the MCGM, namely the… More >

  • Open Access

    ARTICLE

    Efficient Cohomology Computation for Electromagnetic Modeling

    Paweł Dłotko1, Ruben Specogna2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 247-278, 2010, DOI:10.3970/cmes.2010.060.247

    Abstract The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddy-current formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-calledthick cutsare needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick cuts automatically. Nevertheless, none of the approaches proposed in literature meet all the requirements of being automatic, computationally efficient and general. In this paper, an automatic, computationally efficient… More >

  • Open Access

    ARTICLE

    Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm

    Liviu Marin1

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.060.221

    Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical convergence, stability and accuracy of… More >

  • Open Access

    ARTICLE

    Unconditionally Stable Convergence with Power Principle-based Time-Integration Schemes

    G. Formica1, F. Milicchio2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 199-220, 2010, DOI:10.3970/cmes.2010.060.199

    Abstract This manuscript introduces a novel sufficient condition for the unconditionally stable convergence of the general class of trapezoidal integrators. Contrary to standard energy-based approaches, this convergence criterion is derived from the power principles, in terms of both balance and dissipation. This result improves the well-known condition of stable convergence based on the energy method, extending its applicative spectrum to a variety of physical problems, whose constitutive prescriptions may be more appropriately characterized by means of evolving field equations. Our treatment, tailored for generalized trapezoidal integrators, addresses both linear and nonlinear problems, extending its applicability to contexts where standard energy-based schemes… More >

  • Open Access

    ARTICLE

    Finite Element Analysis of Discrete Circular Dislocations

    K.P. Baxevanakis1, A.E. Giannakopoulos2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 181-198, 2010, DOI:10.3970/cmes.2010.060.181

    Abstract The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence of grain boundaries, interstitial particles,… More >

  • Open Access

    ARTICLE

    Sustained Drug Release from Contact Lenses

    J.A.Ferreira2,3, P. Oliveira1, P.M. Silva4, A. Carreira5,3, J.N. Murta6

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 151-180, 2010, DOI:10.3970/cmes.2010.060.151

    Abstract This paper focuses on the release of an ophthalmic drug (flurbiprofen) from a loaded copolymer where the drug is simultaneously dispersed in the polymeric matrix and entrapped in particles. The copolymer is based in 2-hydroxyethyl methacrylate co-methacrylic acid and silicone is used to prepare the loaded particles. A mathematical model to simulate the drug release is proposed and a qualitative analysis is performed. In vitro experimental results are compared with simulation results. Contact lens made from the presented copolymer are expected to deliver drug at therapeutical levels for a few days. More >

  • Open Access

    ARTICLE

    Reduced Polynomials and Their Generation in Adomian Decomposition Methods

    Jun-Sheng Duan1, Ai-Ping Guo2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 139-150, 2010, DOI:10.3970/cmes.2010.060.139

    Abstract Adomian polynomials are constituted of reduced polynomials and derivatives of nonlinear operator. The reduced polynomials are independent of the form of the nonlinear operator. A recursive algorithm of the reduced polynomials is discovered and its symbolic implementation by the software Mathematica is given. As a result, a new and convenient algorithm for the Adomian polynomials is obtained. More >

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