A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. T...A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation(single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for ...A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries (KdV) equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation (nonlinear convectiondiffusion problems) and the KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
In this article,an accurate Chebyshev finite spectral method for the 2-D extended Boussinesq equations is proposed.The method combines the advantages of both the finite difference and spectral methods.The Adams-Bashfo...In this article,an accurate Chebyshev finite spectral method for the 2-D extended Boussinesq equations is proposed.The method combines the advantages of both the finite difference and spectral methods.The Adams-Bashforth predictor and the fourth-order Adams-Moulton corrector are adopted for the numerical solution of the governing differential equations.An efficient wave absorption strategy is also proposed to effectively absorb waves at outgoing wave boundaries and reflected waves from the interior of the computational domain due to barriers and bottom slopes at the incident wave boundary to avoid contamination of the specified incident wave conditions.The proposed method is verified by a case where experimental data are available for comparison for both regular and irregular waves.The case is wave diffraction over a shoal reported by Vincent and Briggs.Numerical results agree very well with the corresponding experimental data.展开更多
Guided waves are generally considered as a powerful approach for crack detection in structures,which are commonly investigated using the finite element method(FEM).However,the traditional FEM has many disadvantages in...Guided waves are generally considered as a powerful approach for crack detection in structures,which are commonly investigated using the finite element method(FEM).However,the traditional FEM has many disadvantages in solving wave propagation due to the strict requirement of mesh density.To tackle this issue,this paper proposes an efficient time-domain spectral finite element method(SFEM)to analyze wave propagation in cracked structures,in which the breathing crack is modeled by definiiig the spectral gap element.Moreover,novel orthogonal polynomials and Gauss-Lobatto-Legendre quadrature rules are adopted to construct the spectral element.Meanwhile,a separable hard contact is utilized to simulate the breathing behavior.Finally,a comparison of the numerical results between the FEM and the SFEM is conducted to demonstrate the high efficiency and accuracy of the proposed method.Based on the developed SFEM,the nonlinear features of waves and influence of the incident mode are also studied in detail,which provides a helpful guide for a physical understanding of the wave propagation behavior in structures with breathing cracks.展开更多
This paper uses the spectral stochastic finite element method(SSFEM)for analyzing reinforced concrete(RC)beam/slab problems.In doing so,it presents a new framework to study how the correlation length of a random field...This paper uses the spectral stochastic finite element method(SSFEM)for analyzing reinforced concrete(RC)beam/slab problems.In doing so,it presents a new framework to study how the correlation length of a random field(RF)with uncertain parameters will affect modeling uncertainties and reliability evaluations.It considers:1)different correlation lengths for uncertainty parameters,and 2)dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete structures.To show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability,two examples of RC beams and slabs have been investigated.According to the results,the RF correlation length is effective in modeling uncertainties and evaluating reliabilities;the longer the correlation length,the greater the dispersion range of the structure response and the higher the failure probability.展开更多
The effect of the turbulence intensity of the oncoming stream on the aerodynamic characteristics of the NACA-0012 airfoil is investigated by a direct numerical simulation. The numerical results are found to be consist...The effect of the turbulence intensity of the oncoming stream on the aerodynamic characteristics of the NACA-0012 airfoil is investigated by a direct numerical simulation. The numerical results are found to be consistent with the experimental measurements. Based on the finite spectral QUICK scheme, the simulation gets the high accuracy results. Both the simulation and the experiment reveal that the airfoil stall does not exist for the low turbulence intensity, however, occurs when the turbulence intensity increases sufficiently. Besides, the turbulence intensity has a significant effect on both the airfoil boundary layer and the separated shear layer.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10272118) the Hong Kong Polytechnic University Research Grant (No.A-PE28) the Research Fund for the Doctoral Program of Ministry of Education of China (No.20020558013)
文摘A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation(single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.
基金supported by the Research Grants Council of Hong Kong (No. 522007)the National Marine Public Welfare Research Projects of China (No. 201005002)
文摘A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries (KdV) equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation (nonlinear convectiondiffusion problems) and the KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.
基金Project supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No. PolyU5220/07E)the National Marine Public Welfare Research Projects of China (Grant No. 201005002)
文摘In this article,an accurate Chebyshev finite spectral method for the 2-D extended Boussinesq equations is proposed.The method combines the advantages of both the finite difference and spectral methods.The Adams-Bashforth predictor and the fourth-order Adams-Moulton corrector are adopted for the numerical solution of the governing differential equations.An efficient wave absorption strategy is also proposed to effectively absorb waves at outgoing wave boundaries and reflected waves from the interior of the computational domain due to barriers and bottom slopes at the incident wave boundary to avoid contamination of the specified incident wave conditions.The proposed method is verified by a case where experimental data are available for comparison for both regular and irregular waves.The case is wave diffraction over a shoal reported by Vincent and Briggs.Numerical results agree very well with the corresponding experimental data.
基金the National Natural Sclenee Foundation of China(Grant No.51704222)China Pastdoctoral Science Foundation(Grant No.2018M633570)Fundamental Research Funds for the Cemtal Unveritiee(Grant No.3102017090004).
文摘Guided waves are generally considered as a powerful approach for crack detection in structures,which are commonly investigated using the finite element method(FEM).However,the traditional FEM has many disadvantages in solving wave propagation due to the strict requirement of mesh density.To tackle this issue,this paper proposes an efficient time-domain spectral finite element method(SFEM)to analyze wave propagation in cracked structures,in which the breathing crack is modeled by definiiig the spectral gap element.Moreover,novel orthogonal polynomials and Gauss-Lobatto-Legendre quadrature rules are adopted to construct the spectral element.Meanwhile,a separable hard contact is utilized to simulate the breathing behavior.Finally,a comparison of the numerical results between the FEM and the SFEM is conducted to demonstrate the high efficiency and accuracy of the proposed method.Based on the developed SFEM,the nonlinear features of waves and influence of the incident mode are also studied in detail,which provides a helpful guide for a physical understanding of the wave propagation behavior in structures with breathing cracks.
文摘This paper uses the spectral stochastic finite element method(SSFEM)for analyzing reinforced concrete(RC)beam/slab problems.In doing so,it presents a new framework to study how the correlation length of a random field(RF)with uncertain parameters will affect modeling uncertainties and reliability evaluations.It considers:1)different correlation lengths for uncertainty parameters,and 2)dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete structures.To show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability,two examples of RC beams and slabs have been investigated.According to the results,the RF correlation length is effective in modeling uncertainties and evaluating reliabilities;the longer the correlation length,the greater the dispersion range of the structure response and the higher the failure probability.
基金Project supported by the National Natural Science Foundation of China(No.108720006)the National Basic Research Program of China(973 Program)(No.2007CB714601)
文摘The effect of the turbulence intensity of the oncoming stream on the aerodynamic characteristics of the NACA-0012 airfoil is investigated by a direct numerical simulation. The numerical results are found to be consistent with the experimental measurements. Based on the finite spectral QUICK scheme, the simulation gets the high accuracy results. Both the simulation and the experiment reveal that the airfoil stall does not exist for the low turbulence intensity, however, occurs when the turbulence intensity increases sufficiently. Besides, the turbulence intensity has a significant effect on both the airfoil boundary layer and the separated shear layer.