Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 79-106, 2010, DOI:10.3970/cmes.2010.059.079

Abstract Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.
In previous work [Lucas, P.,Bijl, H., and Zuijlen, A.H. van(2010)], we have shown that a Jacobian-free Newton-Krylov (JFNK) algorithm, preconditioned with an approximate factorization of the Jacobian which approximately matches the target residual operator, enables a speed up of a factor of 10 compared to nonlinear multigrid (NMG) for two-dimensional, large Reynolds number, unsteady flow computations. Furthermore, in [Lucas, P., Zuijlen, A.H. van, and Bijl, H. (2010)] we show that this algorithm also greatly outperforms NMG for parameter… More >

Alfredo Nicolás¹, Blanca Bermúdez², Elsa Báez³

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 83-106, 2009, DOI:10.3970/cmes.2009.048.083

Abstract Numerical results of natural convection flows in two-dimensional cavities, filled with air, are presented to study the effects on the characteristics of the flows as some parameters vary: the Rayleigh number Ra and the aspect ratio A of the cavity. This kind of thermal flows may be modeled by the unsteady Boussinesq approximation in stream function-vorticity variables. The results are obtained with a simple numerical scheme, previously reported for isothermal/mixed convection flows, based mainly on a fixed point iterative process applied to the non-linear elliptic system that results after time discretization. The evolution of the flows, mainly flows converging to… More >

Marco La Mantia¹, Peter Dabnichki^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 131-154, 2008, DOI:10.3970/cmes.2008.033.131

Abstract A potential flow based boundary element method was devised to obtain the hydrodynamic forces acting on oscillating wings. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the flapping wing and proposed earlier by the authors, is implemented in the numerical procedure. A comparison with published experimental data (Read et al., 2003) is carried out and the three-dimensional computational results showed good agreement, especially if compared with a similar two-dimensional numerical approach (La Mantia and Dabnichki, 2008) and the potential analytical model of Garrick (1936). The need of considering the differences… More >

S.P. Hu¹, D.L. Young², C.M. Fan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 1-20, 2008, DOI:10.3970/cmes.2008.024.001

Abstract In this paper, a novel numerical scheme called (FDMFS), which combines the finite difference method (FDM) and the method of fundamental solutions (MFS), is proposed to simulate the nonhomogeneous diffusion problem with an unsteady forcing function. Most meshless methods are confined to the investigations of nonhomogeneous diffusion equations with steady forcing functions due to the difficulty to find an unsteady particular solution. Therefore, we proposed a FDM with Cartesian grid to handle the unsteady nonhomogeneous term of the equations. The numerical solution in FDMFS is decomposed into a particular solution and a homogeneous solution. The particular solution is constructed using… More >

J. M. F. Trindade¹, J. C. F. Pereira²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 1-10, 2007, DOI:10.3970/cmes.2007.020.001

Abstract In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model… More >

Rosario M. A. Marretta¹, Giovanni Lombardi², Roberto Antinoro¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 73-84, 2003, DOI:10.3970/cmes.2003.004.073

Abstract An approach based on Lighthill's transpiration velocity is explored and proposed for a new design criterion for airfoils in unsteady and viscous flows. This criterion confines its methodologies to the close proximity of the laminar and turbulent boundary layer and it shows good efficiency in predicting and calculating the wake evolution regions in a wide range of operating unsteady parameters. Also, the criterion is capable of predicting low Mach number, attached flow-fields as accurately as the full Navier-Stokes solutions when the massive flow separation is avoided. The agreement of the present results with those empirically and theoretically determined is very… 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 >

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 >

Mohd Imran Ansari^1,*, Syed Fahad Anwer¹

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.4, pp. 259-279, 2018, DOI:10.32604/fdmp.2018.03891

Abstract We have conducted a numerical study to investigate the relationship between the aerodynamic performance of an insect wing section and the effect of corrugation in gliding flight. In particular, an Airfoil-CR, corresponding to Kesel’s Profile 2 (Kesel, Journal of Experimental Biology, vol. 203, 2000), has been used. This profile represents exactly the cross section of the so-called “Aeshna cyanea”. A smoothed variant of this profile (referred to in the present study as Airfoil-SM) has also been considered. Introducing five different variants of the Airfoil-CR corresponding to different levels of corrugation, namely M1, M2, M3, M4 and M5, an unsteady fluid… More >

G. Venkata Ramana Reddy^1,*, Y. Hari Krishna¹

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.3, pp. 213-222, 2018, DOI: 10.3970/fdmp.2018.00411

Abstract The objective of the present problem is to investigate a two-dimensional unsteady flow of a viscous incompressible electrically conducting fluid over a stretching surface taking into account a transverse magnetic field of constant strength. Applying the similarity transformation, the governing boundary layer equations of the problem converted into nonlinear ordinary differential equations and then solved numerically using fourth order Runge-Kutta method with shooting technique. The effects of various parameters on the velocity and temperature fields as well as the skin-friction coefficient and Nusselt number are presented graphically and discussed qualitatively. More >