Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 147-176, 2009, DOI:10.3970/cmes.2009.041.147

Abstract Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This paper, therefore, extends the strategy proposed by [Aftosmis and Berger (2002)] to compute the refinement threshold. The extended strategy computes the refinement threshold based on a user desired number of grid cells and adaptations, thereby ensuring high computational efficiency. Because our main interest is flow around wind turbines, the adaptation strategy has been optimized for flow More >

D. L. Young^1,3, K. H. Chen², T. Y. Liu³, L. H. Shen³, C. S. Wu³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 225-270, 2009, DOI:10.3970/cmes.2009.040.225

Abstract In this article, a hypersingular meshless method (HMM) is extended to solve 3D potential problems for arbitrary domains after a 2D model was successfully developed (Young et al. 2005a). The solutions are represented by a distribution of the double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions (MFS). By using the desingularization technique to regularize the singularity and hypersingularity of the double layer potentials, the source points can be located exactly on the real boundary to avoid the sensitivity of locating fictitious boundary for putting… More >

Sen Yung Lee¹, Jyh Shyang Wu²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 133-154, 2009, DOI:10.3970/cmes.2009.040.133

Abstract The three coupled governing differential equations for the in-plane vibrations of curved non-uniform Timoshenko beams are derived via the Hamilton's principle. Three physical parameters are introduced to simplify the analysis. By eliminating all the terms with the axial displacement parameter, then reducing the order of differential operator acting on the flexural displacement parameter, one uncouples the three governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in term of the angle of the rotation due to bending for the first time. The explicit relations between More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 125-154, 2009, DOI:10.3970/cmes.2009.039.125

Abstract We propose a new numerical method for solving the boundary value problems of ordinary differential equations (ODEs) under multipoint boundary conditions specified at t = T_i, i = 1,...,m, where T₁ < ... < T_m. The finite difference scheme is used to approximate the ODEs, which together with the m-point boundary conditions constitute a system of nonlinear algebraic equations (NAEs). Then a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the new approach is highly accurate and efficient with a fast convergence. The FTIM can also be used to find More >

N. Armour¹, S. Dost^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.4, pp. 331-344, 2009, DOI:10.3970/fdmp.2009.005.331

Abstract A combined numerical and experimental investigation has been undertaken to explore the benefits of an applied static magnetic field on Silicon transport into a Germanium melt. This work utilized a similar material configuration to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The measured concentration profiles from the samples processed with and without the application of magnetic field showed very similar shape. The amount of silicon transport into the melt is slightly higher in the samples processed under magnetic field, and there is a substantial difference in dissolution interface… More >

R. Djebali^1,2, M. El Ganaoui^2,3, H. Sammouda¹, R. Bennacer⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.3, pp. 261-282, 2009, DOI:10.3970/fdmp.2009.005.261

Abstract The simplified thermal lattice Boltzmann model (STLBM) developed by Peng, Shu and Chew (2003) is used in this work to simulate low-Rayleigh-number natural convection in a heated rectangular cavity on a uniform grid. It is shown how by resorting to the double populations approach both hydrodynamic and thermal fields can be effectively simulated. Furthermore, a general benchmark is carried out to account for the effect of different parameters in relatively wide ranges. Results are compared with previous works available in the literature. More >

K.H. Chen^1,2, J.H. Kao³, J.T. Chen⁴

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 253-280, 2009, DOI:10.3970/cmc.2009.009.253

Abstract In this paper, solving antiplane piezoelectricity problems with multiple inclusions are attended by using the regularized meshless method (RMM). This is made possible that the troublesome singularity in the MFS disappears by employing the subtracting and adding-back techniques. The governing equations for linearly electro-elastic medium are reduced to two uncoupled Laplace's equations. The representations of two solutions of the two uncoupled system are obtained by using the RMM. By matching interface conditions, the linear algebraic system is obtained. Finally, typical numerical examples are presented and discussed to demonstrate the accuracy of the solutions. More >

Chein-ShanLiu¹

CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 219-234, 2009, DOI:10.3970/cmc.2009.013.219

Abstract The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the More >

Brent L. Adams, Joshua Kacher

CMC-Computers, Materials & Continua, Vol.14, No.3, pp. 185-196, 2009, DOI:10.3970/cmc.2009.014.185

Abstract Consideration is given to the resolution of dislocation density afforded by EBSD-based scanning electron microscopy. Comparison between the conventional Hough- and the emerging high-resolution cross-correlation-based approaches is made. It is illustrated that considerable care must be exercised in selecting a step size (Burger's circuit size) for experimental measurements. Important variables affecting this selection include the dislocation density and the physical size and density of dislocation dipole and multi-pole components of the structure. It is also illustrated that simulations can be useful to the interpretation of experimental recoveries. More >

Chih-Ping Wu^1,2, Shao-En Huang²

CMC-Computers, Materials & Continua, Vol.12, No.3, pp. 251-282, 2009, DOI:10.3970/cmc.2009.012.251

Abstract A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, doubly curved functionally graded (FG) piezo-thermo-elastic shells under thermal loads. Four different loading conditions, applied on the lateral surfaces of the shells, are considered. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of multilayered composite elastic plates/shells, is modified to be feasible for the present analysis of FG piezo-thermo-elastic plates/shells. The modifications include that a displacement-based formulation More >