Home / Journals / CMES / Vol.44, No.3, 2009
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  • Open Access

    ARTICLE

    Numerical Study of Residual Correction Method Applied to Non-linear Heat Transfer Problem

    Chia-Yi Cheng, Cha’o-Kuang Chen1, Yue-Tzu Yang
    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 203-218, 2009, DOI:10.3970/cmes.2009.044.203
    Abstract This paper seeks to utilize the residual correction method in coordination with the evolutionary monotonic iteration technique to obtain upper and lower approximate solutions of non-linear heat transfer problem of the annular hyperbolic profile fins whose thermal conductivity vary with temperature. First, the monotonicity of a non-linear differential equation is reinforced by using the monotone iterative technique. Then, the cubic spline method is applied to discretize and convert the differential equation into the mathematical programming problems. Finally, based on the residual correction concept, the complicated constraint inequality equations can be transferred into the simple iterative equations. As verified by this… More >

  • Open Access

    ARTICLE

    A Galerkin-RBF Approach for the Streamfunction-Vorticity-Temperature Formulation of Natural Convection in 2D Enclosured Domains

    D. Ho-Minh1, N. Mai-Duy1, T. Tran-Cong1
    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 219-248, 2009, DOI:10.3970/cmes.2009.044.219
    Abstract This paper reports a new discretisation technique for the streamfunc -tion-vorticity-temperature (ψ−ω−T) formulation governing natural convection defined in 2D enclosured domains. The proposed technique combines strengths of three schemes, i.e. smooth discretisations (Galerkin formulation), powerful high-order approximations (one-dimensional integrated radial-basis-function networks) and pressure-free low-order system (ψ−ω−T formulation). In addition, a new effective way of deriving computational boundary conditions for the vorticity is proposed. Two benchmark test problems, namely free convection in a square slot and a concentric annulus, are considered, where a convergent solution for the former is achieved up to the Rayleigh number of 108. More >

  • Open Access

    ARTICLE

    An Optimal Fin Design Problem in Estimating the Shapes of Longitudinal and Spine Fully Wet Fins

    Cheng-Hung Huang1, Yun-Lung Chung1
    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 249-280, 2009, DOI:10.3970/cmes.2009.044.249
    Abstract The optimum shapes for the longitudinal and spine fully wet fins are estimated in the present inverse design problem by using the conjugate gradient method (CGM) based on the desired fin efficiency and fin volume. One of the advantages in using CGM in the inverse design problem lies in that it can handle problems having a large number of unknown parameters easily and converges very fast. Results obtained by using the CGM to solve the inverse design problems are justified based on the numerical experiments. Results show that when the Biot number and relative humidity are varied, the optimum fin… More >

  • Open Access

    ARTICLE

    On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales

    Chein-Shan Liu1, Weichung Yeih2, Satya N. Atluri3
    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 281-312, 2009, DOI:10.3970/cmes.2009.044.281
    Abstract Here we develop a general purpose pre/post conditionerT, to solve an ill-posed system of linear equations,Ax=b. The conditionerTis obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to:Ty=x, whereyis the vector of coefficients in the Trefftz expansion, andxis the boundary data at the discrete points on a unit circle. We show that the quality of the conditionerTis greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show thatTcan be multiplicatively decomposed into a dilationTDand a rotationTR. For an odd-orderedA, we develop four conditioners based on… More >

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