H. Naj^1,2,3, G. Mompean^1,2

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 >

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 >

Yongchang Cai^1,2, 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 >

Bhaskar Kumar¹, Sanjay Mittal^1,2

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 >

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 >

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): F_i(x_j) = 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 ∂F_i/∂x_j 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 >

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 >

Yu Miao¹, Qiao Wang¹, Bihai Liao^1,2, 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 >

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 >

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 Ra_c and the critical wave… More >