G. Kosec¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 191-216, 2009, DOI:10.3970/cmes.2009.047.191

Abstract This paper explores an application of a novel mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [Sarler and Vertnik (2006)] in solution of coupled heat transfer and fluid flow problems with solid-liquid phase change. The melting/freezing of a pure substance is solved in primitive variables on a fixed grid with convection suppression, proportional to the amount of the solid fraction. The involved temperature, velocity and pressure fields are represented on overlapping 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… More >

D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 219-248, 2009, DOI:10.3970/cmes.2009.044.219

Abstract This paper reports a new discretisation technique for the streamfunc -tion-vorticity-temperature (ψ−ω−T) formulation governing natural convection defined in 2D enclosured domains. The proposed technique combines strengths of three schemes, i.e. smooth discretisations (Galerkin formulation), powerful high-order approximations (one-dimensional integrated radial-basis-function networks) and pressure-free low-order system (ψ−ω−T formulation). In addition, a new effective way of deriving computational boundary conditions for the vorticity is proposed. Two benchmark test problems, namely free convection in a square slot and a concentric annulus, are considered, where a convergent solution for the former is achieved up to the Rayleigh number of 10⁸. More >

R. Avila¹, F.J. Solorio¹

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 177-202, 2009, DOI:10.3970/cmes.2009.044.177

Abstract Heat transfer processes involving phase change either, solidification or melting, appear frequently in nature and in industrial applications. In this paper the convective patterns that arise from a 2D shear driven annular flow (without and with melting), are presented. The convective annular flow with radial gravity can be considered as a simplified model of the atmospheric flow in the terrestrial equatorial plane (bounded by the warm surface of the Earth and the cold tropopause). The governing equations have been numerically solved by the Spectral Element Method. The numerical results reported in this paper, for the cases without melting (at two… More >

Briti Sundar Deb¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179

Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

G. Kosec¹, B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.3, pp. 197-208, 2008, DOI:10.3970/cmes.2008.025.197

Abstract This paper explores the application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of coupled heat transfer and fluid flow problems in Darcy porous media. The involved temperature, velocity and pressure fields are represented on overlapping 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 energy and momentum equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local continuity equation violation. This formulation does not require… More >

Haruhiko Kohno, Takahiko Tanahashi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 155-170, 2001, DOI:10.3970/cmes.2001.002.155

Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10^-2, Marangoni number Ma = 0.0 - 6.2067 × 10², Grashof number Gr = 7.1104 × 10⁶, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σ_T =0.0 - 1.5 × 10^-5N/mK. Although the velocity… More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 45-60, 2000, DOI:10.3970/cmes.2000.001.205

Abstract Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multi-dimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convection-diffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems. More >

T. Ozawa¹, N. Ishigami¹, Y. Hayakawa², T. Koyama², M. Kumagawa²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 1-6, 2000, DOI:10.3970/cmes.2000.001.161

Abstract To investigate the solution convection in the rotational Bridgman method, both flow patterns and temperature distributions were calculated by solving three equations in 3-dimensional analysis: Navier-Stokes, continuity and energy. We focused on the relationship between ampoule rotational rate and temperature distribution in the growth solution reservoir. In the 3-dimensional model, In-Ga-Sb solution was put between GaSb seed and feed crystals, where seed and feed crystals were cylindrical in shape, and the In-Ga-Sb solution was semi-cylindrical. The ampoule rotational rate was changed in a range of 0 to 100 rpm. By increasing the ampoule rotational rate, the flow velocity in the… More >

Sacia Kachi^1,*, Fatima-zohra Bensouici¹, Nawel Ferroudj¹, Saadoun Boudebous²

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.2, pp. 89-105, 2019, DOI:10.32604/fdmp.2019.00263

Abstract The objective of the present study is to analyze the laminar mixed convection in a square cavity with moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall while all the other horizontal sides of the cavity are considered adiabatic. The numerical method is based on a finite difference technique where the spatial partial derivatives appearing in the governing equations are discretized using a high order scheme, and time advance is dealt with by a fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative… More >

Toufik Benmalek¹, Ferhat Souidi¹, Mourad Moderres^2,*, Bilal Yassad¹, Said Abboudi³

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.2, pp. 107-123, 2019, DOI:10.32604/fdmp.2019.04496

Abstract This study aims to analyze mixed convection in a square cavity with two moving vertical walls by finite volume method. The cavity filled with Non-Newtonian fluid of Bingham model is heated from below and cooled by the other walls. This study has been conducted for certain parameters of Reynolds number (Re=1-100), Richardson number (Ri=1-20), Prandtl number (Pr=1-500), and Bingham number has been studied from 0 to 10. The results indicate that the increase in yield stress drops the heat transfer and the flow become flatter, while increasing Reynolds number augments it. The convective transport is dominant when increasing Richardson number… More >