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  • Open Access

    ARTICLE

    Computation of the Turbulent Flow in a Square Duct Using a Cubic Low-Reynolds Stress Model

    H. Naj1,2,3, G. Mompean1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 181-206, 2009, DOI:10.3970/cmes.2009.053.181

    Abstract The aim of this work is to predict numerically the turbulent flow through a straight square duct using a nonlinear stress-strain model. The paper considers the application of the Craft et al.'s model [Craft, Launder, and Suga (1996)] to the case of turbulent incompressible flow in a straight square duct. In order to handle wall proximity effects, damping functions are introduced. Using a priori and a posteriori investigations, we show the performance of this model to predict such flows. The analysis of the flow anisotropy is made using the anisotropy-invariant map proposed by Lumley and Newman [Lumley and Newman (1977)].… More >

  • Open Access

    ARTICLE

    A Thermal Tomography Problem in Estimating the Unknown Interfacial Enclosure in a Multiple Region Domain with an Internal Cavity

    Cheng-Hung Huang1, Meng-Ting Chaing1

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 153-180, 2009, DOI:10.3970/cmes.2009.053.153

    Abstract A three-dimensional thermal tomography problem (or inverse geometry problem) in estimating the unknown irregular shape of interfacial enclosure (or surface) for a multiple region domain with an internal cavity by using the steepest descent method (SDM) and a general purpose commercial code CFD-ACE+ is examined in the present work based on the simulated measured temperature distributions on the outer surface obtained by infrared thermography. The advantage of calling CFD-ACE+ as a subroutine in this thermal tomography problem lies in its characteristics of easily-handling the moving boundary problem considered here since it has the function of automatic grid generation. Three test… More >

  • Open Access

    ARTICLE

    Large Deformation Analyses of Space-Frame Structures, with Members of arbitrary Cross-Section, Using Explicit Tangent Stiffness Matrices, Based on a von Karman Type Nonlinear Theory in Rotated Reference Frames

    Yongchang Cai1,2, J.K. Paik3, Satya N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 123-152, 2009, DOI:10.3970/cmes.2009.053.123

    Abstract This paper presents a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A co-rotational reference frame, involving the axes of each finitely rotated beam finite-element, is used as the Updated Lagrangian reference frame for the respective element. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. An assumed displacement approach is used to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix… More >

  • Open Access

    ARTICLE

    Convectively Unstable Anti-Symmetric Waves in Flows Past Bluff Bodies

    Bhaskar Kumar1, Sanjay Mittal1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 95-122, 2009, DOI:10.3970/cmes.2009.053.095

    Abstract The steady flow past a circular cylinder is investigated. Symmetry conditions are imposed along the centerline of the flow field. The variation of the structure of the recirculation zone with the Reynolds number is studied. The effect of the location of lateral boundary on the flow is analyzed and compared with results from earlier studies. The eddy length varies linearly with Re. Three kinds of solutions, based on eddy structure, are found for different location of the lateral boundary. Global linear stability analysis has been carried out in a translating frame to determine the convective modes for flow past a… More >

  • Open Access

    ARTICLE

    Slow Rotation of an Axisymmetric Slip Particle about Its Axis of Revolution

    Yi W. Wan1, Huan J. Keh2

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 73-94, 2009, DOI:10.3970/cmes.2009.053.073

    Abstract The problem of the rotation of a rigid particle of revolution about its axis in a viscous fluid is studied theoretically in the steady limit of low Reynolds number. The fluid is allowed to slip at the surface of the particle. A singularity method based on the principle of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution for the fluid velocity field that satisfies the boundary condition at infinity. The slip condition on the surface of… More >

  • Open Access

    ARTICLE

    A Scalar Homotopy Method for Solving an Over/Under-Determined System of Non-Linear Algebraic Equations

    Chein-Shan Liu1, Weichung Yeih2, Chung-Lun Kuo3, Satya N. Atluri4

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 47-72, 2009, DOI:10.3970/cmes.2009.053.047

    Abstract Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): Fi(xj) = 0, i, j = 1,... ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one to solve the NAEs, due to the ease of its numerical implementation. However, this type of algorithm is sensitive to the initial guess of solution, and is expensive in terms of the computations of the Jacobian matrix ∂Fi/∂xj and its inverse at each iterative step. In addition, the Newton-like methods restrict one to construct an iteration procedure for n-variables by using n-equations,… More >

  • Open Access

    ARTICLE

    Solution Methods for Nonsymmetric Linear Systems with Large off-Diagonal Elements and Discontinuous Coefficients

    Dan Gordon1, Rachel Gordon2

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 23-46, 2009, DOI:10.3970/cmes.2009.053.023

    Abstract Linear systems with very large off-diagonal elements and discontinuous coefficients (LODC systems) arise in some modeling cases, such as those involving heterogeneous media. Such problems are usually solved by domain decomposition methods, but these can be difficult to implement on unstructured grids or when the boundaries between subdomains have a complicated geometry. Gordon and Gordon have shown that Björck and Elfving's (sequential) CGMN algorithm and their own block-parallel CARP-CG are very robust and efficient on strongly convection dominated cases (but without discontinuous coefficients). They have also shown that scaling the equations by dividing each equation by the L2-norm of its… More >

  • Open Access

    ARTICLE

    A Dual Hybrid Boundary Node Method for 2D Elastodynamics Problems

    Yu Miao1, Qiao Wang1, Bihai Liao1,2, Junjie Zheng1

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.053.001

    Abstract As a truly meshless method, the Hybrid Boundary Node method (Hybrid BNM) does not require a `boundary element mesh', either for the purpose of interpolation of the solution variables or for the integration of `energy'. This paper presents a further development of the Hybrid BNM to the 2D elastodynamics. Based on the radial basis function (RBF) and the Hybrid BNM, it presents an inherently meshless, boundary-only technique, which named dual hybrid boundary node method (DHBNM), for solving 2D elastodynamics. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method (DRM), while the general solution… More >

  • Open Access

    ARTICLE

    Solid Element with Four-Point Integration in Plane for Bulk Forming

    Ting Du1, J. P. Xu1, Y.Q. Liu2, Z. B. Zhang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 93-114, 2009, DOI:10.3970/cmes.2009.051.093

    Abstract An eight-node hexahedral element with four-point quadrature in plane is developed using the assumed strain method, which can eliminate volumetric locking of incompressible material and absence of the portion of shear velocity strain related with hourglass mode to suppress hourglass mode and shear locking. In this approach, the radial return algorithm is adopted for more precise calculation of internal forces, stress and strain. In addition, a co-rotational coordinates system is established to make bending simulation much more effective, and the system is applicable to arbitrary 3D anisotropic yield criteria. A large elastic-plastic deformation of unconstrained thick plate bending example is… More >

  • Open Access

    ARTICLE

    The Chebyshev Tau Spectral Method for the Solution of the Linear Stability Equations for Rayleigh-Bénard Convection with Melting

    Rubén Avila1, Eduardo Ramos2, S. N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 73-92, 2009, DOI:10.3970/cmes.2009.051.073

    Abstract A Chebyshev Tau numerical algorithm is presented to solve the perturbation equations that result from the linear stability analysis of the convective motion of a fluid layer that appears when an unconfined solid melts in the presence of gravity. The system of equations that describe the phenomenon constitute an eigenvalue problem whose accurate solution requires a robust method. We solve the equations with our method and briefly describe examples of the results. In the limit where the liquid-solid interface recedes at zero velocity the Rayleigh-Bénard solution is recovered. We show that the critical Rayleigh number Rac and the critical wave… More >

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