Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 53-66, 2007, DOI:10.3970/cmes.2007.021.053

Abstract A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equation, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accurate as one desired. Then, we use the collocation method and the Galerkin method to derive linear equations system to determine the Fourier coefficients. Here, the factor… More >

Chein-Shan Liu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 111-122, 2007, DOI:10.3970/cmes.2007.020.111

Abstract A highly accurate new solver is developed to deal with interior and exterior mixed-boundary value problems for two-dimensional Laplace equation, including the singular ones. To promote the present study, we introduce a circular artificial boundary which is uniquely determined by the physical problem domain, and derive a Dirichlet to Robin mapping on that artificial circle, which is an exact boundary condition described by the first kind Fredholm integral equation. As a consequence, we obtain a modified Trefftz method equipped with a characteristic length factor, ensuring that the new solver is stable because the condition number can be greatly reduced. Then,… More >

Igor Patlashenko¹, Dan Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 61-70, 2000, DOI:10.3970/cmes.2000.001.221

Abstract The method of Absorbing Boundary Conditions (ABCs) is considered for the numerical solution of a class of nonlinear exterior wave scattering problems. Recently, a scheme based on the exact nonlocal Dirichlet-to-Neumann (DtN) ABC has been proposed for such problems. Although this method is very accurate, it is also highly expensive computationally. In this paper, the nonlocal ABC is replaced by a low-order local ABC, which is obtained by localizing the DtN condition in a certain "optimal'' way. The performance of the new local scheme is compared to that of the nonlocal scheme via numerical experiments in two dimensions. More >

Nouri Sabrina^1,*, Abderrahmane Ghezal¹, Said Abboudi², Pierre Spiteri³

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.2, pp. 121-135, 2018, DOI: 10.3970/fdmp.2018.02045

Abstract This paper deals with the numerical study of heat and mass transfer occurring in a cavity filled with a low Prandtl number liquid. The model includes the momentum, energy and mass balance equations. These equations are discretized by a finite volume technique and solved in the framework of a custom SIMPLER method developed in FORTRAN. The effect of the problem characteristic parameters, namely the Lewis and Prandtl numbers, on the instability of the flow and related solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for values of the… More >

Meryem NAOUM¹, Mustapha EL ALAMI²

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.2, pp. 56-68, 2016, DOI:10.3970/fdmp.2016.012.056

Abstract A numerical study of mixed convection from a U-shaped channel is carried out. The flow is considered two dimensionnel. The inlet opening is adjusted in the right vertical part of the channel, while the outlet one is placed on the left vertical part. Navier–Stokes equations are solved using a control volume method and the SIMPLEC algorithm is considered for the treatment of pressure–velocity coupling. Special emphasis is given to detail the effect of the Reynolds and Rayleigh numbers on the heat transfer generated by mixed convection. The results are given for the parameters of control as, Rayleigh number (5.10³≤Ra≤10⁷), Prandtl… More >

ADNANI Massinissa¹, MEZIANI Bachir², OURRAD Ouerdia², ZITOUNE Mounir¹

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.1, pp. 1-14, 2016, DOI:10.3970/fdmp.2016.012.001

Abstract A numerical study of natural convection in a square cavity subjected to the thermals boundary conditions on the sidewalls is presented and discussed. The fluid is Newtonian and equations governing the flow field and the heat transfer are given in dimensionless form. The finite volume method was adopted to solve the algebraic system. Influence of the Prandtl and the Rayleigh numbers on heat transfer and the flow field is illustrated and discussed as the stream functions, isotherms, horizontal velocity, local and average Nusselt numbers. Results indicate that improved heat transfer is more pronounced with increasing Rayleigh number. In particular, at… More >

Hawa Singh¹, Paras Ram², Vikas Kumar³

FDMP-Fluid Dynamics & Materials Processing, Vol.10, No.4, pp. 521-550, 2014, DOI:10.3970/fdmp.2014.010.521

Abstract The fluctuating flow produced by magneto - hydrodynamic free convection past an impulsively started isothermal vertical plate is studied taking into account the effects of radiation and viscous dissipation. By using the similarity transformation, the governing equations are transformed into dimensionless form and then the system of nonlinear partial differential equations is solved by a perturbation technique. The considered uniform magnetic field acts perpendicular to the plate, which absorbs the fluid with a given suction velocity. A comparison is made in velocity and temperature profiles for two particular cases of real and imaginary time dependent functions. The effects of various… More >

F. Mechighel^1,2, M. El Ganaoui¹, M. Kadja², B. Pateyron³, S. Dost⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.4, pp. 313-330, 2009, DOI:10.3970/fdmp.2009.005.313

Abstract A numerical study has been carried out to investigate the three-dimen -sional buoyant flow in a parallelepiped box heated from below and partially from the two sidewalls (a configuration commonly used for solidification problems and crystal growth systems). Attention has been paid, in particular, to phenomena of symmetry breaking and transition to unsteady non-symmetric convection for a low Prandtl number fluid (Pr=0.01). The influence of an applied horizontal magnetic field on the stability properties of the flow has been also considered. Results obtained may be summarized as follows: In the absence of magnetic field and for relatively small values of… More >

Nadia Dihmani¹, Samir Amraqui¹, Ahmed Mezrhab^1,2, Najib Laraqi³

FDMP-Fluid Dynamics & Materials Processing, Vol.8, No.3, pp. 311-322, 2012, DOI:10.3970/fdmp.2012.008.311

Abstract Natural convection with surface radiation heat transfer is investigated numerically in a vented vertical channel heated asymmetrically. The numerical solution is obtained using a finite volume method based on the SIMPLER algorithm for the treatment of velocity-pressure coupling. Concerning the radiation exchange, in particular, the working fluid is assumed to be transparent, so that only the solid surfaces (assumed diffuse-grey) give a contribute to such exchange. The effect of Rayleigh numbers and rib width (for Pr=0.7 air fluid) on the heat transfer and flow structure in the channel is examined in detail. Results are presented in terms of isotherms, streamlines,… More >

CMC-Computers, Materials & Continua, Vol.52, No.2, pp. 123-131, 2016, DOI:10.3970/cmc.2016.052.123

Abstract In this paper, the gyrotropic bi-anisotropy of the chiral medium in substrate constitutive parameters (xc and hc) of a rectangular microstrip patch antenna is introduced in order to observe its effects on the complex resonant frequency and half-power bandwidth. The analysis is based on the full-wave spectral domain approach using the Moment Method, with sinusoidal type basis functions. The numerical calculations related to the dominant mode have been carried out, and it has been observed that the resonant frequency and the bandwidth are directly linked to the medium chirality. The new results can be considered as a generalisation form of… More >