CMES-Vol. 80, Nos. 3&4, 2011

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Is the Karman Mode the Least Stable Mode Below the Critical Re?
Sushil Mohan Ratnaker¹, Sanjay Mittal^1,2
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 < Re_cr. 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… More >

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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 >

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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 More >

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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 More >

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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 More >

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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 Liu^1,2, 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 Vector More >

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