L. Dong¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 1-44, 2012, DOI:10.3970/cmes.2012.085.001

Abstract In this paper, a generalized Trefftz method in plane elasticity is developed, for solving problems in an arbitrary multiply connected domain. Firstly, the relations between Trefftz basis functions from different source points are discussed, by using the binomial theorem and the logarithmic binomial theorem. Based on these theorems, we clearly explain the relation between the T-Trefftz and the F-Trefftz methods, and why the traditional T-Trefftz method, which uses only one source point, cannot successfully solve problems in a multiply connected domain with genus larger than 1. Thereafter, a generalized Trefftz method is proposed, which uses logarithmic and negative power series… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 575-602, 2012, DOI:10.3970/cmes.2012.084.575

Abstract An iterative algorithm based on the concept of best descent vector u in x^· = λu is proposed to solve a system of nonlinear algebraic equations (NAEs): F(x) = 0. In terms of the residual vector F and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm evolves. A new method to approximate the best descent vector is developed, and we find a critical value of the weighting parameter α_c in the best descent vector u = α_cF + B^TF,… More >

C.S. Nor Azwadi¹, N.I.N. Izual²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 559-574, 2012, DOI:10.3970/cmes.2012.084.559

Abstract Natural convection in a differentially heated enclosure plays vital role in engineering applications such as nuclear reactor, electronic cooling technologies, roof ventilation, etc. The developed thermal flow patterns induced by the density difference are expected to be critically dependence on the inclination angles of the cavity. Hence, thermal and fluid flow pattern inside a differentially heated side enclosure walls with various inclination angles have been investigated numerically using the mesoscale lattice Boltzmann scheme. Three different dimensionless Rayleigh numbers were used, and a dimensionless Prandtl number of 0.71 was set to simulate the circulation of air in the system. It was… More >

N. Thai-Quang¹, K. Le-Cao¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 528-558, 2012, DOI:10.3970/cmes.2012.084.528

Abstract This study is concerned with the development of integrated radial-basis-function (IRBF) method for the simulation of two-dimensional steady-state incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, a high-order compact local IRBF scheme is employed to represent the convection and diffusion terms. Furthermore, an effective boundary treatment for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, is proposed. This transformation is based on global 1D-IRBF approximators using values of the pressure at interior nodes along a grid line and first-order derivative values of the pressure at the two… More >

Ridha Djebali^1,2, Mohamed ElGanaoui³, Taoufik Naffouti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 499-527, 2012, DOI:10.3970/cmes.2012.084.499

Abstract A thermal lattice Boltzmann model for incompressible flow is developed and extended to investigate the natural convection flow in porous media under the effect of uniform magnetic field. The study shows that the flow behaviour is various parameters dependent. The Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da) and the medium inclination angle from the horizontal (Φ), the magnetic field orientation (ψ) and the medium porosity (ε) effects are carried out in wide ranges encountered in industrial and engineering applications. It was found that the flow and temperature patterns change significantly when varying these parameters. To confirm the accuracy… More >

Hong-Hua Dai^1,2, Matt Schnoor², Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459

Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method, the collocation-resulting nonlinear algebraic… More >

C.K. Chao¹, A. Wikarta¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 439-458, 2012, DOI:10.3970/cmes.2012.084.439

Abstract An analytical solution to a three-phase composite with an eccentric circular inclusion under a remote uniform shear load is given in this work. Mode-III stress intensity factors for an arbitrarily oriented crack embedded in an infinite matrix or a core inclusion are provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation located either in the core inclusion or in the infinite matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack are established by using the screw… More >

Ayşe Gül Kaplan¹, Yılmaz Dereli

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423

Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature. More >

Gusein Sh. Guseinov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405

Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 383-404, 2012, DOI:10.3970/cmes.2012.084.383

Abstract An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value α_c in the critical descent vector u = α_cr + B^Tr is derived, which renders the largest convergence rate as to be the globally optimal iterative algorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u = αr + B^Tr to solve the ill-posed linear problems. Some numerical examples are used to reveal… More >