N. Mai-Duy, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 85-102, 2003, DOI:10.3970/cmes.2003.004.085

Abstract This paper reports a mesh-free Indirect Radial Basis Function Network method (IRBFN) using Thin Plate Splines (TPSs) for numerical solution of Differential Equations (DEs) in rectangular and curvilinear coordinates. The adjustable parameters required by the method are the number of centres, their positions and possibly the order of the TPS. The first and second order TPSs which are widely applied in numerical schemes for numerical solution of DEs are employed in this study. The advantage of the TPS over the multiquadric basis function is that the former, with a given order, does not contain the adjustable shape parameter (i.e. the… More >

Enzo TONTI¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237

Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one obtained with FEM, using the… More >

W.W. Liou¹, Y.C. Fang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 119-128, 2000, DOI:10.3970/cmes.2000.001.571

Abstract A simple implicit treatment for the low speed inflow and outflow boundary conditions for the direct simulation Monte Carlo (DSMC) of the flows in microelectromechanical systems (MEMS) is proposed. The local mean flow velocity, temperature, and number density near the subsonic boundaries were used to determine the number of molecules entering the computational domain and their corresponding velocities at every sample average step. The proposed boundary conditions were validated against micro-Poiseuille flows and micro-Couette flows. The results were compared with analytical solutions derived from the Navier-Stokes equations using first-order and second order slip-boundary conditions. The results show that the implicit… More >

J. Sladek¹, V. Sladek¹, V. Kompis², R. Van Keer³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 1-8, 2000, DOI:10.3970/cmes.2000.001.453

Abstract This paper presents an application of a direct Trefftz method with domain decomposition to the two-dimensional elasticity problem. Trefftz functions are substituted into Betti's reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and approximation of boundary quantities. Numerical… More >

A.N. Gulluoglu¹, C.T. Tsai²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 85-90, 2000, DOI:10.3970/cmes.2000.001.085

Abstract Twins in growing crystals are due to excessive thermal stresses induced by the temperature gradients developed during the growth process. Twinning is an important defect in advanced semiconductor crystals such as GaAS and InP. The objective of this study is to develop a computational model to predict the twin formation in the Gallium Arsenide (GaAs) crystals grown by the vertical gradient freeze method (VGF). A quantitative quasi-steady state thermal stress model is developed here for predicting the twinning formation in GaAs grown by VGF. The thermoelastic stresses in VGF grown crystal are calculated from a two-dimensional finite element analysis. Deformation… More >

J.J. Derksen¹, D. Eskin²

FDMP-Fluid Dynamics & Materials Processing, Vol.7, No.4, pp. 341-356, 2011, DOI:10.3970/fdmp.2011.007.341

Abstract Direct simulations of laminar solid-liquid flow in micro-channels with full resolution of the solid-liquid interfaces have been performed. The solids phase consists of simple agglomerates, assembled of monosized, spherical particles. The flow of the interstitial liquid is solved with the lattice-Boltzmann method. Solids and fluid dynamics are two-way coupled. The simulations keep track of the flow-induced forces in the agglomerates. The effects of agglomerate type (doublets, triplets, and quadruplets), solids loading, and channel geometry on (the statistics of the) flow and collision-induced forces have been investigated. By comparing these forces with agglomerate strength, we would be able to assess the… 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 idea of launching a call… More >

K. Achoubir¹, R. Bennacer², A. Cheddadi¹, M. El Ganaoui³, E. Semma^3,4

FDMP-Fluid Dynamics & Materials Processing, Vol.4, No.3, pp. 199-210, 2008, DOI:10.3970/fdmp.2008.004.199

Abstract The present work is devoted to the numerical investigation of the interaction between thermal and solutal convection in enclosures used for modeling directional solidification. The full transient Navier--Stokes, energy and species conservation equations are solved numerically by using finite volumes technique. More >

A. Filali¹, L. Khezzar^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.3, pp. 307-329, 2013, DOI:10.3970/fdmp.2013.009.307

Abstract Numerical investigations of purely-elastic instabilities occurring in creeping flows are reported in planar cross-slot geometries with both sharp and round corners. The fluid is described by the upper-convected Maxwell model, and the governing equations are solved using the finite element technique based on a steady (non-iterative) direct solver implemented in the POLYFLOWcommercial software (version 14.0). Specifically, extensive simulations were carried out on different meshes, with and without the use of flow perturbations, for a wide range of rheological parameters. Such simulations show the onset of flow asymmetries above a critical Deborah number (De). The effect of rounding the corners is… More >

H. Altenbach¹, V. A. Eremeyev²

CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 153-178, 2009, DOI:10.3970/cmc.2009.009.153

Abstract Within the framework of the direct approach to the plate theory we consider natural oscillations of plates made of functionally graded materials taking into account both the rotatory inertia and the transverse shear stiffness. It is shown that in some cases the results based on the direct approach differ significantly from the classical estimates. The reason for this is the non-classical computation of the transverse shear stiffness. More >