A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversi...A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.展开更多
The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a ...The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.展开更多
This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed...This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.展开更多
An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. ...An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method （CSM） is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.展开更多
This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip veloc...This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.展开更多
The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic （MHD） micropolar fluid over a vertical heated nonisothermal stretching surface in the ...The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic （MHD） micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.展开更多
A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet.The considered non-Newtonian fluid has Prandtl number larger than one.The effects of variable fluid properties ...A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet.The considered non-Newtonian fluid has Prandtl number larger than one.The effects of variable fluid properties and heat generation/absorption are also discussed.The balance equations for fluid flow are reduced to a set of ordinary differential equations through a similarity transformation and solved numerically using a Chebyshev spectral scheme.The effect of various parameters on the rate of heat transfer in the thermal boundary regime is investigated,i.e.,thermal conductivity,the heat generation/absorption ratio and the mixed convection parameter.Good agreement appears to exist between theoretical predictions and the existing published results.展开更多
In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use linear transformation to make the interval into a fixed interval [-1,...In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use linear transformation to make the interval into a fixed interval [-1, 1]. Then we use the Gauss quadrature formula to approximate the solution. With the help of lemmas, we get the result that the numerical error decay exponentially in the infinity norm and the Chebyshev weighted Hilbert space norm. Some numerical experiments are given to confirm our theoretical prediction.展开更多
In this paper,we firstly present a novel simple method based on a Picard integral type formulation for the nonlinear multi-dimensional variable coefficient fourthorder advection-dispersion equation with the time fract...In this paper,we firstly present a novel simple method based on a Picard integral type formulation for the nonlinear multi-dimensional variable coefficient fourthorder advection-dispersion equation with the time fractional derivative order a2(1,2).A new unknown function v(x,t)=■u(x,t)/■t is introduced and u(x,t)is recovered using the trapezoidal formula.As a result of the variable v(x,t)are introduced in each time step,the constraints of traditional plans considering the non-integer time situation of u(x,t)is no longer considered.The stability and solvability are proved with detailed proofs and the precise describe of error estimates is derived.Further,Chebyshev spectral collocation method supports accurate and efficient variable coefficient model with variable coefficients.Several numerical results are obtained and analyzed in multi-dimensional spatial domains and numerical convergence order are consistent with the theoretical value 3-a order for different a under infinite norm.展开更多
The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s...The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s early calculations, which also shows that the numerical program is reliable. It is further shown that there is a critical value for the effect of Stokes number, which is about 2. The most damped mode occurs when Stokes number is of order of 10 for different particle concentrations and depends weakly on the wave number. The difference in the eigenfunctions and its derivatives between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is significant.展开更多
In this paper,we apply a new modification of the Adomian decomposition method for solving the problem of boundary layer convective heat transfer with viscous dissipation and low pressure gradient over a at plate.The t...In this paper,we apply a new modification of the Adomian decomposition method for solving the problem of boundary layer convective heat transfer with viscous dissipation and low pressure gradient over a at plate.The technique is based on the standard Adomian decomposition method and the Chebyshev pseudospectral method.Comparisons are made between the pro-posed technique,the standard Adomian decomposition method,and the numerical solutions to demonstrate the applicability,validity,and high accuracy of the present approach.The results demonstrate that the new modification is more efficient and converges faster than the Adomian decomposition method.展开更多
基金Supported by:Joint Research Fund for Earthquake Science,launched by the National Natural Science Foundation of China and the China Earthquake Administration under Grant No.U2039208。
文摘A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.
基金supported by the National Basic Research Program of China (Grant 2013CB733004)
文摘The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.
基金National Natural Science Foundation of China(51076006)
文摘This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.
基金Project supported by the National Natural Science Foundation of China(No.51176026)the Fundamental Research Funds for the Central Universities(No.DUT14RC(3)029)
文摘An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method （CSM） is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.
文摘This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.
文摘The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic （MHD） micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.
文摘A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet.The considered non-Newtonian fluid has Prandtl number larger than one.The effects of variable fluid properties and heat generation/absorption are also discussed.The balance equations for fluid flow are reduced to a set of ordinary differential equations through a similarity transformation and solved numerically using a Chebyshev spectral scheme.The effect of various parameters on the rate of heat transfer in the thermal boundary regime is investigated,i.e.,thermal conductivity,the heat generation/absorption ratio and the mixed convection parameter.Good agreement appears to exist between theoretical predictions and the existing published results.
基金Supported by Guangdong Provincial Education Projects(2021KTSCX071,HSGDJG21356-372)Project of Hanshan Normal University(521036).
文摘In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use linear transformation to make the interval into a fixed interval [-1, 1]. Then we use the Gauss quadrature formula to approximate the solution. With the help of lemmas, we get the result that the numerical error decay exponentially in the infinity norm and the Chebyshev weighted Hilbert space norm. Some numerical experiments are given to confirm our theoretical prediction.
文摘In this paper,we firstly present a novel simple method based on a Picard integral type formulation for the nonlinear multi-dimensional variable coefficient fourthorder advection-dispersion equation with the time fractional derivative order a2(1,2).A new unknown function v(x,t)=■u(x,t)/■t is introduced and u(x,t)is recovered using the trapezoidal formula.As a result of the variable v(x,t)are introduced in each time step,the constraints of traditional plans considering the non-integer time situation of u(x,t)is no longer considered.The stability and solvability are proved with detailed proofs and the precise describe of error estimates is derived.Further,Chebyshev spectral collocation method supports accurate and efficient variable coefficient model with variable coefficients.Several numerical results are obtained and analyzed in multi-dimensional spatial domains and numerical convergence order are consistent with the theoretical value 3-a order for different a under infinite norm.
基金supported by the National Natural Science Foundation of China (Grant Nos.50806023,50721005)the Program of Introducing Talents of Discipline to Universities,(111 Program,Grant No.B06019),China
文摘The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s early calculations, which also shows that the numerical program is reliable. It is further shown that there is a critical value for the effect of Stokes number, which is about 2. The most damped mode occurs when Stokes number is of order of 10 for different particle concentrations and depends weakly on the wave number. The difference in the eigenfunctions and its derivatives between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is significant.
文摘In this paper,we apply a new modification of the Adomian decomposition method for solving the problem of boundary layer convective heat transfer with viscous dissipation and low pressure gradient over a at plate.The technique is based on the standard Adomian decomposition method and the Chebyshev pseudospectral method.Comparisons are made between the pro-posed technique,the standard Adomian decomposition method,and the numerical solutions to demonstrate the applicability,validity,and high accuracy of the present approach.The results demonstrate that the new modification is more efficient and converges faster than the Adomian decomposition method.
