F. Bulut^1,2, Ö. Oruç³, A. Esen³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 263-284, 2015, DOI:10.3970/cmes.2015.108.263

Abstract In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn’t use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L₂ and L_∞ error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for the problems under… More >

Chia-Ming Fan^1,2, Yu-Kai Huang¹, Po-Wei Li¹, Ying-Te Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.6, pp. 491-515, 2015, DOI:10.3970/cmes.2015.105.491

Abstract In this paper, the boundary knot method (BKM) is adopted for accurately analyzing two-dimensional Stokes flows, dominated by viscous force and pressure gradient force. The Stokes flows, which denoted the flow fields with extremely viscous fluid or with very small velocity, appear in various engineering applications, such that it is very important to develop an efficient and accurate numerical method to solve the Stokes equations. The BKM, which can avoid the controversial fictitious boundary for sources, is an integral-free boundary-type meshless method and its solutions are expressed as linear combinations of nonsingular general solutions for Stokes equations. The weighting coefficients… More >

Vinita Chellappan¹, S. Gopalakrishnan¹ and V. Mani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 131-174, 2014, DOI:10.3970/cmes.2014.097.131

Abstract The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical… More >

Po-Wei Li¹, Chia-Ming Fan^1,2, Chun-Yu Chen¹, Cheng-Yu Ku¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 319-350, 2014, DOI:10.3970/cmes.2014.101.319

Abstract A combination of the generalized finite difference method (GFDM), the implicit Euler method and the Newton-Raphson method is proposed to efficiently and accurately analyze the density-driven groundwater flows. In groundwater hydraulics, the problems of density-driven groundwater flows are usually difficult to be solved, since the mathematical descriptions are a system of time- and space-dependent nonlinear partial differential equations. In the proposed numerical scheme, the GFDM and the implicit Euler method were adopted for spatial and temporal discretizations of governing equations. The GFDM is a newly-developed meshless method and is truly free from time-consuming mesh generation and numerical quadrature. Based on… More >

W.L.A. Pereira¹, V.J. Karam², J.A.M. Carrer³, C.S.G. Monteiro¹, W.J. Mansur¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 117-130, 2013, DOI:10.3970/cmes.2013.096.117

Abstract In this work, the BEM is applied to obtain the numerical solutions for free vibration analysis of thick square plates with two edges simply supported or clamped, and the other two edges free. A formulation based on Reissner’s theory is used here, which includes the contribution of the additional translational inertia terms to the integral equation of displacements and internal forces. The boundary element method is used to discretize the space, where it is employed the static fundamental solution. In literature, the responses for the kind of problem addressed here are very important in the hydroelastic analysis of very large… More >

J.L. Morales¹, J.A. Moreno², F. Alhama³

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 1-18, 2011, DOI:10.3970/cmes.2011.076.001

Abstract Following the rules of the network simulation method, a general purpose network model is designed and numerically solved for linear elastostatic problems formulated by the Navier equations. Coupled and nonlinear terms of the PDE, as well as boundary conditions, are easily implemented in the model by means of general purpose electrical devices named controlled current (or voltage) sources. The complete model is run in the commercial software PSPICE and the numerical results are post-processed by MATLAB to facilitate graphical representation. To demonstrate the reliability and efficiency of the proposed method two applications are presented: a cantilever loaded at one end… More >

Ayşe Gül Kaplan¹, Yılmaz Dereli

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423

Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature. 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 >