Q. G. Liu¹, B. Šarler^1,2,3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.4, pp. 235-266, 2013, DOI:10.3970/cmes.2013.091.235

Abstract The purpose of the present paper is development of a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional isotropic linear elasticity problems. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacement of the concentrated point sources by distributed sources over circular discs around the singularity, as originally suggested by [Liu (2010)] for potential problems. The Kelvin’s fundamental solution is employed in collocation of the governing plane strain force balance equations. In case of the displacement boundary conditions, the values of distributed sources are calculated directly and analytically.… More >

M. Razzaq¹, C. Tsotskas², S. Turek¹, T. Kipouros², M. Savill², J. Hron³

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.4, pp. 303-337, 2013, DOI:10.3970/cmes.2013.090.303

Abstract The integration and application of a new multi-objective tabu search optimization algorithm for Fluid Structure Interaction (FSI) problems are presented. The aim is to enhance the computational design process for real world applications and to achieve higher performance of the whole system for the four considered objectives. The described system combines the optimizer with a well established FSI solver which is based on the fully implicit, monolithic formuFlation of the problem in the Arbitrary Lagrangian-Eulerian FEM approach. The proposed solver resolves the proposed fluid-structure interaction benchmark which describes the self-induced elastic deformation of a beam attached to a cylinder in… More >

Cui Li¹, Deli Gao¹, Zhiyong Wu¹, Binbin Diao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.1, pp. 39-56, 2012, DOI:10.3970/cmes.2012.089.039

Abstract At present, a relief well is the most reliable method to control serious blowout accidents, and it is necessary to detect very accurately the relative position of the relief well and the blowout well. The detection tool should be capable of detecting directly the relative distance and direction between the relief well and the blowout well. Its detection accuracy should also meet the engineering demand of drilling a relief well. Using the working principle of a proposed detection tool, this paper analyzes the spread and attenuation laws of the current injected by a single-electrode or three-electrode array in the relief… More >

M. Khezri¹, Z. Vrcelj¹, M.A. Bradford^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 271-306, 2012, DOI:10.3970/cmes.2012.087.271

Abstract A finite strip method (FSM) utilising the generalised reproducing kernel particle method (RKPM) [Behzadan, Shodja, and Khezri (2011)] is developed for the bending analysis of thin plates. In this innovative approach, the spline functions in the conventional spline finite strip method (SFSM) are replaced with generalised RKPM 1-D shape functions in the longitudinal direction, while the transverse cubic functions which are used in the conventional formulations are retained. Since the generalised RKPM is one of the class of meshfree methods which deal efficiently with derivative-type essential boundary conditions, its introduction in the FSM is beneficial for solving boundary value problems… More >

LiviuMarin ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203

Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, the numerical solutions obtained by… More >

Michael J. Rodgers¹, Leon M. Keer, Herbert S. Cheng

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.4, pp. 483-496, 2002, DOI:10.3970/cmes.2002.003.483

Abstract The steady-state temperature rise due to frictional heating on the surface of coated halfspaces and halfplanes is described by closed form expressions in the Fourier transformed frequency domain. These frequency response functions (FRFs) include the effects of the coating and the speed of the moving heat source and apply for all Peclet number regimes. Analytical inversion of these expressions for several special cases shows the Green's functions as infinite series of images, which may be costly and slowly convergent. Also, the influence coefficients integrated from these Green's functions are not available in closed form. Applying fast Fourier transform (FFT) methods… More >

António Tadeu^1,2, Julieta António¹, Patrícia Ferreira³

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.3, pp. 153-176, 2013, DOI:10.3970/cmes.2013.091.153

Abstract This paper presents an iterative coupling between a formulation based on the normal derivative of the integral equation (TBEM) and the method of fundamental solutions (MFS) for the transient analysis of acoustic wave propagation problems in the presence of multiple inclusions. The proposed formulation overcomes the individual limitations of each method, requires less computer memory and may use less CPU time than a full direct coupling formulation scheme. In the proposed formulation each inclusion is solved individually, successively, using the TBEM or the MFS and scatters a field that it is seen as an incident field at each of the… More >

W.J. Santos¹ , J.A.F. Santiago¹, J.C.F Telles¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 23-40, 2012, DOI:10.3970/cmes.2012.087.023

Abstract The aim of this paper is to present numerical simulations of Cathodic Protection (CP) Systems using a Genetic Algorithm (GA) and the Method of Fundamental Solutions (MFS). MFS is used to obtain the solution of the associated homogeneous equation with the non-homogeneous equation subject to nonlinear boundary conditions defined as polarization curves. The adopted GA minimizes a nonlinear error function, whose design variables are the coefficients of the linear superposition of fundamental solutions and the positions of the source points, located outside the problem domain. In this work, the anodes added to the CP system are considered as point sources… More >

C.-D. Tran¹, N. Mai-Duy^1,1, K. Le-Cao¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 499-520, 2012, DOI:10.3970/cmes.2012.085.499

Abstract A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is… More >

Ali Shokri¹, Mehdi Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 333-358, 2012, DOI:10.3970/cmes.2012.084.333

Abstract The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method. More >