Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.047.001

Abstract In this paper an analytical method for approximating the solution of backward heat conduction problem is presented. The Fourier series expansion technique is used to formulate a first-kind Fredholm integral equation for the temperature field u(x,t) at any time t < T, when the data are specified at a final time T. Then we consider a direct regularization, instead of the Tikhonov regularization, by adding the term αu(x,t) to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us by transforming it to a two-point boundary value problem, and thus a closed-form solution More >

R. Vertnik¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 65-96, 2009, DOI:10.3970/cmes.2009.044.065

Abstract The application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent flow is explored in this paper. The turbulent flow equations are described by the low - Re number k-emodel with Jones and Launder [Jones and Launder (1971)] closure coefficients. The involved velocity, pressure, turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The velocity, turbulent kinetic energy and… More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 229-252, 2009, DOI:10.3970/cmc.2009.009.229

Abstract When the given input data are corrupted by an intensive noise, most numerical methods may fail to produce acceptable numerical solutions. Here, we propose a new numerical scheme for solving the Burgers equation forward in time and backward in time. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ )u(x,t) =: v(x,t,τ), such that the original Burgers equation is written as a new parabolic type partial differential equation in the space of (x,t,τ). A fictitious damping coefficient can be used to strengthen the stability in the numerical integration… More >

Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3

CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 111-136, 2009, DOI:10.3970/cmc.2009.009.111

Abstract In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution C^α(x,t) are provided 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 >

Xiaoyi Liang¹, Zhen Yang^1,2, Xingsheng Gu³, Licheng Ling¹

CMC-Computers, Materials & Continua, Vol.13, No.2, pp. 135-152, 2009, DOI:10.3970/cmc.2009.013.135

Abstract Supercapacitors, also called electrical double-layer capacitors (EDLCs), occupy a region between batteries and dielectric capacitors on the Ragone plot describing the relation between energy and power. BET specific surface area and specific capacitance are two important electrochemical property parameters for activated carbon EDLCs, which are usually tested by experimental method. However, it is misspent time to repeat lots of experiments for EDLCs' studies. In this investigation, we developed one theoretical model based on improved particle swarm optimization algorithm back propagation (PSO-BP) neural network (NN) to simulate and optimize BET specific surface area and specific capacitance. More >

E.J. Sapountzakis¹, V.G. Mokos¹

CMC-Computers, Materials & Continua, Vol.12, No.2, pp. 157-196, 2009, DOI:10.3970/cmc.2009.012.157

Abstract In this paper a general solution for the elastic buckling analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section subjected to an arbitrary inplane loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well… More >

E.J. Sapountzakis¹, V.G. Mokos²

CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 1-40, 2009, DOI:10.3970/cmc.2009.010.001

Abstract In this paper the boundary element method is employed to develop a displacement solution for the general transverse shear loading problem of composite beams of arbitrary constant cross section. The composite beam (thin or thick walled) consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the… More >

Atsuya Oishi¹, Shinobu Yoshimura²

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.2, pp. 115-132, 2008, DOI:10.3970/cmes.2008.025.115

Abstract This paper describes the finite element analyses of dynamic problems using graphics hardware. The graphics hardware, known as GPU that is an acronym of Graphics Processing Unit, was first developed only for processing 3D computer graphics. However it has obtained both flexible programmability using a high-level shader programming language such as OpenGL Shading Language (GLSL), and has also obtained fast numerical processing ability of over 160 GFLOPS that is much faster than CPU. In this paper, GPU is utilized for the finite element analyses of dynamic problems. Two different computational tasks in the dynamic finite More >

G. Accary¹, S. Meradji², D. Morvan², D. Fougère²

FDMP-Fluid Dynamics & Materials Processing, Vol.4, No.4, pp. 263-270, 2008, DOI:10.3970/fdmp.2008.004.263

Abstract In the literature, only few references have dealt with mixed-convection flows in the low Mach number approximation. For this reason, in the present study we propose to extend the standard 3D benchmark for mixed convection in a rectangular channel heated from below (Medale and Nicolas, 2005) to the case of large temperature variations (for which the Boussinesq approximation is no longer valid). The Navier-Stokes equations, obtained under the assumption of a low Mach number flow, are solved using a finite volume method. The results, corresponding to the steady-state case of the benchmark, lead to the More >