Qifa Lang, Yuqiao Zheng^*, Tiancai Cui, Chenglong Shi, Heyu Zhang

Energy Engineering, Vol.121, No.2, pp. 483-498, 2024, DOI:10.32604/ee.2023.042437

Abstract This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle. We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory (NREL), to research the effects of the nonlinear flap-wise vibration characteristics. The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam, and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first. Then, the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force. Lastly, it is… More >

Jiaqun Wang^1,2, Guanxu Pan², Youhe Zhou², Xiaojing Liu^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.1, pp. 297-318, 2024, DOI:10.32604/cmes.2023.030622

Abstract In this study, a wavelet multi-resolution interpolation Galerkin method (WMIGM) is proposed to solve linear singularly perturbed boundary value problems. Unlike conventional wavelet schemes, the proposed algorithm can be readily extended to special node generation techniques, such as the Shishkin node. Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients. All the shape functions possess the Kronecker delta property, making the imposition of boundary conditions as easy as that in the finite element method. Four numerical examples are studied to demonstrate the validity and accuracy of the proposed… More >

D. Santhi Kumari^a,*, Venkata Subrahmanyam Sajja^a, P. M. Kishore^b,†

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-10, 2021, DOI:10.5098/hmt.16.24

Abstract This study attempts to explore a qualitative analysis of the effects of Soret on an unsteady magnetohydrodynamics free convection flow of a chemically reacting incompressible fluid past an infinite vertical plate embedded in a porous medium taking the source of heat and thermal radiation into account as well as viscous dissipation. The central equations are scrupulously converted into sets of coupled nonlinear partial differential equations for providing logical solutions. The method of Galerkin finite element is used considering appropriate boundary conditions for diverse physical metrics and then numerically analyzed employing MATLAB. A significant change in velocity, temperature, concentration profiles is… More >

Jufeng Wang¹, Yong Wu¹, Ying Xu¹, Fengxin Sun^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 341-356, 2023, DOI:10.32604/cmes.2022.023140

Abstract By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the… More >

Heng Cheng¹, Zebin Xing¹, Miaojuan Peng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 945-964, 2022, DOI:10.32604/cmes.2022.020755

Abstract In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational… More >

Zhijuan Meng¹, Yanan Fang¹, Yumin Cheng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 55-79, 2022, DOI:10.32604/cmes.2022.019828

Abstract In this paper, a fast element-free Galerkin (FEFG) method for three-dimensional (3D) elasticity problems is established. The FEFG method is a combination of the improved element-free Galerkin (IEFG) method and the dimension splitting method (DSM). By using the DSM, a 3D problem is converted to a series of 2D ones, and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems. The essential boundary conditions are treated by the penalty method. The splitting direction uses the finite difference method (FDM), which can… More >

Haishan Lu, Shuguang Gong^*, Jianping Zhang, Guilan Xie, Shuohui Yin

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1151-1178, 2021, DOI:10.32604/cmes.2021.016165

Abstract We proposed an improved graphics processing unit (GPU) acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin (EFG) method. This method can effectively eliminate the race condition under parallelization. We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model. We explored the GPU parallel algorithm of assembling stiffness matrix, solving discrete equation, analyzing sensitivity, and updating design variables in detail. We also proposed a node pair-wise method for assembling the stiffness matrix and a node-wise method for sensitivity analysis to eliminate race conditions during the parallelization. Furthermore, we… More >

W. M. Abd-Elhameed^1,2,*, Asmaa M. Alkenedri²

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603

Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely, Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based on making use of the power series representations and inversion formulas of these classes of polynomials. The derived formulas serve in converting the even-order… More >

Şuayip Yüzbaşı^{1, *}, Murat Karaçayır¹

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 941-956, 2020, DOI:10.32604/cmes.2020.08938

Abstract In this study, we present a numerical scheme similar to the Galerkin method in order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/2. In this approach, the approximate solution is assumed to have the form of a polynomial in the variable t = x^α , where α is a positive real parameter of our choice. The problem is firstly expressed in vectoral form via substituting the matrix counterparts of the terms present in the equation. After taking inner product of this vector with nonnegative integer powers of t up to a selected positive parameter N,… More >

Zhen Wang^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 353-376, 2020, DOI:10.32604/cmes.2020.08776

Abstract In this paper, a special case of nonlinear time fractional cable equation is studied. For the equation defined on a bounded domain, the existence, uniqueness, and regularity of the solution are firstly studied. Furthermore, it is numerically studied via the weighted and shifted Grünwald difference (WSGD) methods/the local discontinuous Galerkin (LDG) finite element methods. The derived numerical scheme has been proved to be stable and convergent with order O(∆t² + h^k+1), where ∆t, h, k are the time stepsize, the spatial stepsize, and the degree of piecewise polynomials, respectively. Finally, a numerical experiment is presented to verify the theoretical analysis. More >