Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 261-276, 2009, DOI:10.3970/cmes.2009.051.261

Abstract The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is More >

M.V. Menshykova¹, I.A. Guz, O.V. Menshykov

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 239-260, 2009, DOI:10.3970/cmes.2009.051.239

Abstract The present work is devoted to the investigation of the internal instability in laminated materials. The paper is concerned with the development of a unified computational procedure for numerical realisation of the method as applied to various constitutive equations of the layers, different loading schemes (uniaxial or biaxial loading) and different precritical conditions (large or small precritical deformations). It contains many examples of critical stresses/strains calculations for particular composites as well as analysis of different buckling modes. More >

N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 213-238, 2009, DOI:10.3970/cmes.2009.051.213

Abstract This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-function networks (IRBFNs) for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme More >

Chan T.L.^1,2, Xie M.L.^1,3, Cheung C.S.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 191-212, 2009, DOI:10.3970/cmes.2009.051.191

Abstract An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It satisfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is… More >

D.N. Srinath¹, Sanjay Mittal¹, Veera Manek²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 169-190, 2009, DOI:10.3970/cmes.2009.051.169

Abstract A continuous adjoint method is formulated and implemented for the multi-point shape optimization of airfoils at low Re. The airfoil shape is parametrized with a non-uniform rational B-Spline (NURBS). Optimization studies are carried out for two different objective functions. The first involves an inverse function on the lift coefficient over a range of Re. The objective is to determine a shape that results in a lift coefficient of 0.4 at three values of Re: 10, 100 and 500. The second objective involves a direct function on the lift coefficient over a range of angles of More >

E. Mesquita¹, J.Labaki ¹ and L.O.S.Ferreira¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 143-168, 2009, DOI:10.3970/cmes.2009.051.143

Abstract There is a growing trend towards solving problems of computational mechanics by parallelization strategies. The traditional approach is to implement the parallelization procedures on CPUs based on the MPI or OpenMP paradigms. Recent efforts have been made to implement computational tasks on general-purpose programmable graphics hardware (GPGPU). The GPU is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the Longman's integration method on graphics hardware. A serial implementation of Longman's method was rewritten under the SIMD (Single Input Multiple… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇²w + k²q(x)w = 0, x∈ Ω⊂R², B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of More >

Yongchang Cai^1,2, J.K. Paik³, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 335-368, 2009, DOI:10.3970/cmes.2009.054.335

Abstract This paper presents a simple finite element method, based on assumed moments and rotations, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A von Karman type nonlinear theory of deformation is employed in the updated Lagrangian co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. The Reissner variational principle is used in the updated Lagrangian co-rotational reference frame, to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix of the beam element in the co-rotational reference frame. The explicit expression… More >

M. Dumbser¹, D.S. Balsara²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 301-334, 2009, DOI:10.3970/cmes.2009.054.301

Abstract In this article we use the new, unified framework of high order one-step P_NP_M schemes recently proposed for inviscid hyperbolic conservation laws by Dumbser, Balsara, Toro, and Munz (2008) in order to solve the viscous and resistive magnetohydrodynamics (MHD) equations in two and three space dimensions on unstructured triangular and tetrahedral meshes. The P_NP_M framework uses piecewise polynomials of degree N to represent data in each cell and piecewise polynomials of degree M ≥ N to compute the fluxes and source terms. This new general machinery contains usual high order finite volume schemes (N = 0) and discontinuous… More >

Arif Amirov¹, Zekeriya Ustaoglu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 283-300, 2009, DOI:10.3970/cmes.2009.054.283

Abstract We present the solvability of a two space dimensional coefficient inverse problem for a transport-like equation and investigate the approximate solution of this problem with the use of centered difference formulas and a symbolic approximation method. Since this inverse problem is overdetermined, which is the main difficulty in studying of its solvability, it is replaced by a related determined one by using some extension of the class of unknown functions. More >