Home / Journals / CMES / Vol.80, No.3&4, 2011
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  • Open Access

    ARTICLE

    Is the Karman Mode the Least Stable Mode Below the Critical Re?

    Sushil Mohan Ratnaker1, Sanjay Mittal1,2
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 179-200, 2011, DOI:10.3970/cmes.2011.080.179
    Abstract Flow past a circular cylinder looses stability at Re ~ 47 via Hopf bifurcation. The eigenmode responsible for the instability leads to the von Kármán vortex shedding. In this work the linear stability of the flow to other modes, near the critical Re, is investigated. In particular, the study explores the possibility of modes other than the Kármán mode having the largest growth rate for Re < Recr. To this extent, global linear stability analysis (LSA) of the steady flow past a circular cylinder is carried out for Re = 45 and 48. In addition to the Kármán modes, two… More >

  • Open Access

    ARTICLE

    Applicability of the Boundary Particle Method

    F.Z. Wang 1,2,3
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 201-218, 2011, DOI:10.3970/cmes.2011.080.201
    Abstract In this paper, we consider the boundary particle method (BPM) which is excellent in solving inhomogeneous partial differential equations in terms of solution accuracy and simplicity. In order to investigate the applicability of the BPM, we examine the relationship between its solution accuracy and the effective condition number. We show that the effective condition number, which estimates system stability with the right-hand side vector taken into account, is inversely proportional to the root mean square error in the numerical approximation. Moreover, for noisy-boundary cases, we find that the BPM can not yield reasonable results, for more noise added to the… More >

  • Open Access

    ARTICLE

    A Spectrally Accurate Quadrature for 3-D Boundary Integrals

    Gregory Baker1, Huaijian Zhang1
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 219-232, 2011, DOI:10.3970/cmes.2011.080.219
    Abstract Boundary integral methods have proved very useful in the simulation of free surface motion, in part, because only information at the surface is necessary to track its motion. However, the velocity of the surface must be calculated quite accurately, and the error must be reasonably smooth, otherwise the surface buckles as numerical inaccuracies grow, leading to a failure in the simulation. For two-dimensional motion, the surface is just a curve and the boundary integrals are simple poles that may be removed, allowing spectrally accurate numerical integration. For three-dimensional motion, the singularity in the integrand, although weak, presents a greater challenge… More >

  • Open Access

    ARTICLE

    Application of Symmetric Hyperbolic Systems for the Time-Dependent Maxwell's Equations in Bi-Anisotropic Media

    V.G.Yakhno1, T.M. Yakhno2
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 233-250, 2011, DOI:10.3970/cmes.2011.080.233
    Abstract The time-dependent Maxwell's equations in non-dispersive homogeneous bi-anisotropic materials are considered in the paper. These equations are written as a symmetric hyperbolic system. A new method of the computation of the electric and magnetic fields arising from electric current is suggested in the paper. This method consists of the following. The Maxwell's equations are written in terms of the Fourier transform with respect to the space variables. The Fourier image of the obtained system is a system of ordinary differential equations whose coefficients depend on the 3D Fourier parameter. The formula for the solution of the obtained system is derived… More >

  • Open Access

    ARTICLE

    Elasto-Plastic Analysis of Structural Problems Using Atomic Basis Functions

    V. Kozulić1, B. Gotovac1
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 251-274, 2011, DOI:10.3970/cmes.2011.080.251
    Abstract The numerical model for the elasto-plastic analysis of prismatic bars subjected to torsion is developed. The functions implemented in this model are Fup basis functions which belong to the class of atomic functions. The collocation method is used to form a system of equations in which the differential equation of the problem is satisfied in collocation points of closed domain, while boundary conditions are satisfied exactly at the domain boundary. The propagation of plastic zones in the cross-section is monitored by applying the incremental-iterative procedure until failure. An approximate solution of arbitrary accuracy is attained by hierarchically increasing the number… More >

  • Open Access

    ARTICLE

    An Iterative Method Using an Optimal Descent Vector, for Solving an Ill-Conditioned System Bx=b, Better and Faster than the Conjugate Gradient Method

    Chein-Shan Liu1,2, Satya N. Atluri1
    CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 275-298, 2011, DOI:10.3970/cmes.2011.080.275
    Abstract To solve an ill-conditioned system of linear algebraic equations (LAEs): Bx - b = 0, we define an invariant-manifold in terms of r := Bx - b, and a monotonically increasing function Q(t) of a time-like variable t. Using this, we derive an evolution equation for dx / dt, which is a system of Nonlinear Ordinary Differential Equations (NODEs) for x in terms of t. Using the concept of discrete dynamics evolving on the invariant manifold, we arrive at a purely iterative algorithm for solving x, which we label as an Optimal Iterative Algorithm (OIA) involving an Optimal Descent VectorMore >

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