Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 155-170, 2012, DOI:10.3970/cmes.2012.084.155

Abstract In this paper, the homotopy analysis method is applied to analyze the heat transfer of the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. This method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series and the results indicated that the series has high accuracy by comparing it with those generated by the complex More >

J. D. Hales¹, S. R. Novascone¹, R. L. Williamson¹, D. R. Gaston¹, M. R. Tonks¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 123-154, 2012, DOI:10.3970/cmes.2012.084.123

Abstract The equations governing solid mechanics are often solved via Newton's method. This approach can be problematic if the Jacobian determination, storage, or solution cost is high. These challenges are magnified for multiphysics applications. The Jacobian-free Newton-Krylov (JFNK) method avoids many of these difficulties through a finite difference approximation. A parallel, nonlinear solid mechanics and multiphysics application named BISON has been created that leverages JFNK. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and multiphysics applications using a series of demonstration problems. We show that JFNK has More >

Zaobao Liu^1,2, Weiya Xu¹, Jianfu Shao²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 99-122, 2012, DOI:10.3970/cmes.2012.084.099

Abstract In this paper, the Gauss process is proposed for application on landslide displacement analysis and prediction with dynamic crossing validation. The prediction problem using noisy observations is first introduced. Then the Gauss process method is proposed for modeling non-stationary series of landslide displacements based on its ability to model noisy data. The monitoring displacement series of the New Wolong Temple Landslide is comparatively studied with other methods as an instance to implement the strategy of the Gauss process for predicting landslide displacement. The dynamic crossing validation method is adopted to manage the displacement series so… More >

P. L. Bishay¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce… More >

O. Baysal¹, G. Tanoglu²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 27-40, 2012, DOI:10.3970/cmes.2012.084.027

Abstract In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (θ-method). Numerical results that illustrate the good performance of this method are reported. More >

M. Koyuncu¹, F. Y. Ikikat¹, G. C. Icoz², B. Baranoglu³, A. Yazici²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 13-26, 2012, DOI:10.3970/cmes.2012.084.013

Abstract A parallel dual reciprocity boundary element method solution to thermoelasticity and thermoviscoelasticity problems is proposed. The DR-BEM formulation is given in Fourier Transform Space where the Time Space solutions are obtained through inverse Fourier Transform. The parallellization of the code is achieved through solving each frequency at a distinct computational node. The implemented parallel code is tested on 64-core IBM blade servers and it is seen that a linear speed-up is achieved. More >

Etibar S. Panakhov¹, Murat Sat²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 1-12, 2012, DOI:10.3970/cmes.2012.084.001

Abstract In this paper an inverse problem by two given spectrum for a second-order differential operator with coulomb singularity of the type A/x in zero point ( here A is constant), is studied. It is well known that two spectrum {λ_n} and {µ_n} uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0,π]. The aim of this paper is to prove the generalized degeneracy of the kernel K(x,t) . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference q^~(x) - q(x). More >

Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

Ashraf Balabel

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 599-638, 2012, DOI:10.3970/cmes.2012.083.599

Abstract In the present paper, a new generalized level set numerical method based on the Fast Marching Method is developed for predicting the moving interface thermo-fluid dynamics in turbulent free surface flows. The numerical method is devoted to predict the turbulent interfacial dynamics resulting from either aerodynamic force or thermocapillary effects. The unsteady Reynolds averaged Navier-Stokes equations (RANS) and energy equation are coupled with the level set method and solved separately in each phase using the finite volume method on a non-staggered grid system. The application of the fast marching technique enables the fast as well… More >

Y.F. Nie, Y.Q. Li, L. Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 575-598, 2012, DOI:10.3970/cmes.2012.083.575

Abstract In this paper, we introduce the parallel Node-based Local FEM (NLFEM)-a novel version of FEM with natural parallel performances and adaptivity to various complex parallel environments. As a crucial part of 3D NLFEM, the Node-based Local Tetrahedron Mesh Generation (NLTMG) algorithm is presented, where guaranteeing the global conformity of local meshes is a strategy of ensuring the validity of the NLFEM and decoupling the NLFEM. In order to generate conforming local mesh, we search the neighbor nodes by the neighborhood of a corresponding multilevel bucket and then those nodes are Delaunay tetrahedralized by the TetGen. More >