Sushil Mohan Ratnaker¹, Sanjay Mittal^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 179-200, 2011, DOI:10.3970/cmes.2011.080.179

Abstract Flow past a circular cylinder looses stability at Re ~ 47 via Hopf bifurcation. The eigenmode responsible for the instability leads to the von Kármán vortex shedding. In this work the linear stability of the flow to other modes, near the critical Re, is investigated. In particular, the study explores the possibility of modes other than the Kármán mode having the largest growth rate for Re < Re_cr. To this extent, global linear stability analysis (LSA) of the steady flow past a circular cylinder is carried out for Re = 45 and 48. In addition to the Kármán modes, two… More >

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.2, pp. 141-178, 2011, DOI:10.3970/cmes.2011.080.141

Abstract In this paper, 2-node integrated radial basis function elements (IRBFEs) [CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C²-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains. More >

N. Mai-Duy¹, T. Tran-Cong¹, N. Phan-Thien²

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.3&4, pp. 223-236, 2011, DOI:10.3970/cmes.2011.079.223

Abstract This paper presents a new numerical technique for solving the evolution equations in molecular dynamics (MD). The variation of the MD system is represented by radial-basis-function (RBF) equations which are constructed using integrated multiquadric basis functions and point collocation. The proposed technique requires the evaluation of forces once per time step. Several examples are given to demonstrate the attractiveness of the present implementation. More >

K.I. Silva¹, J.C.F. Telles², F.C. Araújo³

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 209-224, 2011, DOI:10.3970/cmes.2011.078.209

Abstract In this work the boundary element method is applied to solve 2D elastoplastic problems. In elastoplastic boundary element analysis, domain integrals have to be calculated to introduce the contribution of yielded zones. Traditionally, the use of internal integration cells have been adopted to evaluate such domain integrals. The present work, however, proposes an alternative cell free strategy based on the OMLS (Orthogonal Moving Least Squares) interpolation, typically adopted in meshless methods. In this approach the definition of points to compute the interpolated value of a function at a given location only depends on their relative distance, without need to define… More >

Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to… More >

P. Maghoul¹, B. Gatmiri^1,2, D. Duhamel¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.1, pp. 51-76, 2011, DOI:10.3970/cmes.2011.078.051

Abstract This paper aims at obtaining boundary integral formulations as well as three dimensional(3D) fundamental solutions for unsaturated soils under dynamic loadings for the first time. The boundary integral equations are derived via the use of the weighted residuals method in a way that permits an easy discretization and implementation in a Boundary Element code. Also, the associated 3D fundamental solutions for such deformable porous medium are derived in Laplace transform domain using the method of Hérmander. The derived results are verified analytically by comparison with the previously introduced corresponding fundamental solutions in elastodynamic limiting case. These solutions can be used,… More >

Chein-Shan Liu¹, Chung-Lun Kuo²

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.1, pp. 57-80, 2011, DOI:10.3970/cmes.2011.077.057

Abstract In this paper, the solutions of inverse Cauchy problems for quasi-linear elliptic equations are resorted to an unusual mixed group-preserving scheme (MGPS). The bottom of a finite rectangle is imposed by overspecified boundary data, and we seek unknown data on the top side. The spring-damping regularization method (SDRM) is introduced by converting the governing equation into a new one, which includes a spring term and a damping term. The SDRM can further stabilize the inverse Cauchy problems, such that we can apply a direct numerical integration method to solve them by using the MGPS. Several numerical examples are examined to… More >

A. Gakwaya¹, H. Sharifi², M. Guillot¹, M. Souli³, F. Erchiqui⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 209-266, 2011, DOI:10.3970/cmes.2011.073.209

Abstract A mechanical computer aided design and engineering system can be used to reduce the design-to-manufacture cycle time in metal forming process. Such a system could be built upon a solid modeling geometry engine and an efficient finite element (FE) solver. The maintenance of a high-quality mesh throughout the analysis is an essential feature of an efficient finite element simulation of large strain metal forming problems. In this paper, a mesh adaptation technique employing the Arbitrary Lagrangian-Eulerian formulation (ALE) is applied to some industrial metal forming problems. An ACIS boundary representation of the solid model is employed. This type of representation… More >

L. Hedhili, A. Sellier, L. Elasmi, F. Feuillebois

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 137-170, 2011, DOI:10.3970/cmes.2011.073.137

Abstract The motion of a solid particle embedded in a viscous fluid in a closed container requires a precise account of wall effects when in creeping flow. The boundary integral method, which amounts to solving a Fredholm integral equation for the stress on the particle and walls, is used here. The accuracy of the method is improved by using curvilinear six-node triangular boundary elements, the size of which is specially adapted to the particle shape and position with respect to walls. The method is applied to resolve the case of a moving particle in a parallelepiped container. It is validated by… More >

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 299-336, 2011, DOI:10.3970/cmes.2011.072.299

Abstract This paper presents a new control-volume discretisation method, based on Cartesian grids and integrated-radial-basis-function elements (IRBFEs), for the solution of second-order elliptic problems in one and two dimensions. The governing equation is discretised by means of the control-volume formulation and the division of the problem domain into non-overlapping control volumes is based on a Cartesian grid. Salient features of the present method include (i) an element is defined by two adjacent nodes on a grid line, (ii) the IRBF approximations on each element are constructed using only two RBF centres (a smallest RBF set) associated with the two nodes of… More >