R. Vodička¹, V. Mantič², F. París²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 173-204, 2007, DOI:10.3970/cmes.2007.017.173

Abstract An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction… More >

Rodica Borcia^1,2, Michael Bestehorn²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.4, pp. 287-294, 2007, DOI:10.3970/fdmp.2007.003.287

Abstract We developed a phase field model for Marangoni convection in compressible fluids of van der Waals type far from criticality. The theoretical description is based on the Navier-Stokes equation with extra terms responsible for describing the Marangoni effect, the classical heat equation, and the continuity equation. The model previously developed for a two-layer geometry is now extended to drops and bubbles. Finally, we report on 2D numerical simulations for drop Marangoni migration in a vertical temperature gradient. More >

Srikrishna Sahu¹, K. Muralidhar¹, P.K. Panigrahi¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.3, pp. 265-286, 2007, DOI:10.3970/fdmp.2007.003.265

Abstract Convection in a differentially heated cavity partly filled with silicone oil has been experimentally studied. The air-oil layers are subjected to a temperature difference in the vertical direction, with the lower wall being heated with respect to the top. The overall geometry is that of an enclosed cavity that is octagonal in plan. Heights of oil layers considered for experiments correspond to 30, 50, and 70% of the vertical cavity dimension. Measurements have been carried out using a shadowgraph technique. A limited number of interferograms have also been recorded. The shadowgraph technique has been validated… More >

Mark Sussman¹, Mitsuhiro Ohta²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 21-36, 2007, DOI:10.3970/fdmp.2007.003.021

Abstract In this paper, we describe new techniques for numerically approximating two-phase flows. Specifically, we present new techniques for treating the viscosity and surface tension terms that appear in the Navier-Stokes equations for incompressible two-phase flow. Our resulting numerical method has the property that results computed using our two-phase algorithm approach the corresponding "one-phase'' algorithm in the limit of zero gas density/viscosity; i.e. the two-phase results approach the one-phase free-boundary results in the limit that the gas is assumed to become a uniform pressure void. By grid convergence checks and comparison with previous experimental data, we More >

T. J. Jaber¹, M. Z. Saghir¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 175-190, 2006, DOI:10.3970/fdmp.2006.002.175

Abstract The study deals with three-dimensional numerical simulations of fluid flow and heat transfer under the effect of a rotating magnetic field (RMF) during the growth of Ge_0.98Si_0.02 by the traveling solvent method (TSM). By using a RMF, an attempt is made to suppress buoyancy convection in the Ge_0.98Si_0.02 solution zone in order to get high quality and homogeneity with a flat growth interface. The full steady-state Navier-Stokes equations, as well as the energy, mass transport and continuity equations, are solved numerically using the finite element method. Different magnetic field intensities (B=2, 4, 10, 15 and 22 More >

P.D. Shah¹, Ch. Song², C.L. Tan¹, X. Wang¹

Structural Durability & Health Monitoring, Vol.2, No.4, pp. 225-238, 2006, DOI:10.3970/sdhm.2006.002.225

Abstract Numerical T-stress solutions in two dimensional anisotropic cracked bodies are very scarce in the literature. Schemes to evaluate this fracture parameter in anisotropy have been reported only fairly recently. Among them are those developed in conjunction with two different computational techniques, namely, the Boundary Element Method (BEM) and the Scaled Boundary Finite-Element Method (SBFEM). This paper provides a review of the respective schemes using these techniques and demonstrates their efficacy with three examples. These examples, which are of engineering importance, involve cracks lying in a homogeneous medium as well as at the interface between dissimilar media. More >

P.D. Shah¹, C.L. Tan^1,2, X. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 185-198, 2006, DOI:10.3970/cmes.2006.013.185

Abstract In this paper, the path independent mutual or M-integral for the computation of the T-stress for interface cracks between dissimilar anisotropic, linear elastic solids, is developed. The required auxiliary field solution is derived from the solution of the problem of an anisotropic composite wedge subjected to a point force at its apex. The Boundary Element Method (BEM) is employed for the numerical stress analysis in which special crack-tip elements with the proper oscillatory traction singularity are used. The successful implementation of the procedure for evaluating the T-stress in a bi-material interface crack and its application are demonstrated More >

S. Masuda¹, H. Noguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 131-144, 2006, DOI:10.3970/cmes.2006.011.131

Abstract This paper presents a novel and accurate technique for modeling discontinuous derivatives in meshfree methods, which will be used in the analysis of structures with material interfaces. The novelty lies in the formulation of the Moving Least Squares Approximation (MLSA) scheme where an introduced discontinuous derivative basis function replaces the conventional linear basis function. Furthermore, it is easy to implement this novelty into existing meshfree methods, such as the Element Free Galerkin (EFG) method, which are based on the MLSA scheme. The successful analyses of one and two-dimensional structures with material interfaces demonstrate the potential More >

Sunil Punjabi¹, K. Muralidhar², P. K. Panigrahi²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.2, pp. 95-106, 2006, DOI:10.3970/fdmp.2006.002.095

Abstract Convection in a differentially heated two-layer system consisting of air and water was studied experimentally, using laser-interferometry. The cavity used for flow visualization was square in cross-section and rectangular in-plan having dimensions of 447 × 32 × 32 mm³. Experiments performed over different layer thicknesses of water filled in a square cross-section cavity, the rest being air, are reported in the present work. The following temperature differences for each layer height were imposed across the hot and the cold walls of the superposed fluid layers: (i) ΔT=10K and (ii)ΔT =18 K. The present study was aimed… More >

K. Matsunaga¹, H. Kawamura¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 59-64, 2006, DOI:10.3970/fdmp.2006.002.059

Abstract Existing studies on solidification phenomena mainly focused on the solidification processes per se. In real systems, however, one cannot neglect the effects of molten material convective flow, such as natural and thermocapillary convection (they strongly affect the resulting quality of the solidified materials). The present study aims to experimentally investigate on the effect of the thermocapillary flow upon the directional solidification in a liquid layer with a free upper surface. If no free surface exists, the solid--liquid interface (SLI) is vertical and straight, while, with the free surface, the SLI is inclined against the wall-normal More >