V. C. Loukopoulos¹, G. C. Bourantas²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 49-70, 2014, DOI:10.3970/cmes.2014.103.049

Abstract A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear… More >

Lei Lu^1,2, Li-Hua Liu^3,4, Xiao-Xiao Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 1-15, 2014, DOI:10.3970/cmes.2014.101.001

Abstract In this paper, we use the modified decomposition method (MDM) to solve the unsteady flow of a nanofluid squeezing between two parallel equations. Copper as nanoparticle with water as its base fluid has considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell- Garnetts (MG) and Brinkman models, respectively. The effects of the squeeze number, the nanofluid volume fraction, Eckert number, δ on Nusselt number and the Prandtl number are investigated. The figures and tables clearly show high accuracy of the method to solve the unsteady flow. More >

N. Thai-Quang¹, N. Mai-Duy¹, C.-D Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.3, pp. 189-220, 2012, DOI:10.3970/cmes.2012.089.189

Abstract In this paper, the alternating direction implicit (ADI) method reported in [You(2006)] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that… More >

Anant Diwakar¹, D. N.Srinath¹, Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 61-90, 2010, DOI:10.3970/cmes.2010.069.061

Abstract Aerodynamic shape optimization of airfoils is carried out for two values of Reynolds numbers: 10³ and 10⁴, for an angle of attack of 5^o. The objective functions used are (a) maximization of lift (b) minimization of drag and (c) minimization of drag to lift ratio. The surface of the airfoil is parametrized by a 4^th order non-uniform rational B-Spline (NURBS) curve with 61 control points. Unlike the efforts in the past, the relatively large number of control points used in this study offer a rich design shape with the possibility of local bumps and valleys on the airfoil surface. The… More >

A. Grimaldi¹, G. Pascazio², M. Napolitano³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.1, pp. 45-56, 2006, DOI:10.3970/cmes.2006.014.045

Abstract This paper provides a numerical method for solving two- and three-dimensional unsteady incompressible flows. The vorticity-velocity formulation of the Navier--Stokes equations is considered, employing the vorticity transport equation and a second-order Poisson equation for the velocity. Second-order-accurate centred finite differences on a staggered grid are used for the space discretization. The vorticity equation is discretized in time using a fully implicit three-level scheme. At each physical time level, a dual-time stepping technique is used to solve the coupled system of non linear algebraic equations by various efficient relaxation schemes. Steady flows are computed by dropping the physical time derivative and… More >

Yoshihiro Ochiai¹, Vladimir Sladek², Jan Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 41-54, 2012, DOI:10.3970/cmes.2012.087.041

Abstract The conventional boundary element method (BEM) requires a domain integral in unsteady thermal stress analysis with heat generation or an initial temperature distribution. In this paper it is shown that the three-dimensional unsteady thermal stress problem can be solved effectively using the triple-reciprocity boundary element method without internal cells. In this method, the distributions of heat generation and initial temperature are interpolated using integral equations and time-dependent fundamental solutions are used. A new computer program was developed and applied to solving several problems. More >

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 311-352, 2012, DOI:10.3970/cmes.2012.083.311

Abstract In this study, local moving least square - one dimensional integrated radial basis function network (LMLS-1D-IRBFN) method is presented and demonstrated with the solution of time-dependent problems such as Burgers' equation, unsteady flow past a square cylinder in a horizontal channel and unsteady flow past a circular cylinder. The present method makes use of the partition of unity concept to combine the moving least square (MLS) and one-dimensional integrated radial basis function network (1D-IRBFN) techniques in a new approach. This approach offers the same order of accuracy as its global counterpart, the 1D-IRBFN method, while the system matrix is more… More >

Hui-Fen Guo^1,2, Bin-Gang Xu^1,3, Sheng-Yan Li¹, Chong-Wen Yu²

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.2, pp. 87-112, 2011, DOI:10.3970/cmes.2011.080.087

Abstract Three-dimensional transient simulation is presented for swirling recirculating flow in a nozzle with a slotted-tube (different grooves) and the effect of the groove number is also investigated. The numerical results on the streamline angles are validated by experimental visualization using the surface oil flow technology. In the downstream center of the injectors, the vortex breakdown experiences a transition from bubble- to spiral- breakdown as time is increased. For all cases under study, as the sizes of two recirculation zones near the injector upstream wall and the step retain almost constant, the spiral breakdown shows a periodic development. The more the… More >

Yoshihiro OCHIAI¹

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.2, pp. 83-102, 2011, DOI:10.3970/cmes.2011.079.083

Abstract In general, internal cells are required to solve unsteady thermo-elasto -plastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. The conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve thermo-elastoplastic problems, because the distribution of initial stress cannot be determined analytically. In this paper, it is shown that two-dimensional unsteady thermo-elastoplastic problems can be solved without the use of internal cells by using the triple-reciprocity BEM and a thin plate spline. The initial stress formulation is adopted and the initial stress… More >

D.M.S. Albuquerque¹, J.M.C. Pereira¹, J.C.F. Pereira^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 337-366, 2011, DOI:10.3970/cmes.2011.072.337

Abstract A numerical study of fluid-structure interaction is presented for the analysis of viscous flow over a resonant membrane airfoil in hovering flight. A flexible membrane moving with a prescribed stroke period was naturally excited to enter into 1st, 2nd and 3rd mode of vibration according to the selected membrane tension. The Navier-Stokes equations were discretized on a moving body unstructured grid using the finite volume method. The instantaneous membrane position was predicted by the 1D unsteady membrane equation with input from the acting fluid flow forces. Following initial validation against reported rigid airfoils predictions, the model is applied to the… More >