Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.展开更多
A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite differen...A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.展开更多
A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few...A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few researches on numerical simulation of Schnakenberg model with spatial fractional order.It is also important to find a simple and effective numerical method.In this paper,the Schnakenberg model is numerically simulated by Fourier spectral method.The Fourier transform is applied to transforming the partial differential equation into ordinary differential equation in space,and the fourth order Runge-Kutta method is used to solve the ordinary differential equation to obtain the numerical solution from the perspective of time.Simulation results show the effectiveness of the proposed method.展开更多
In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence ...In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.展开更多
In this paper,we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation.Using the Strang time-splitting technique,we split the equation into linear part and nonlin...In this paper,we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation.Using the Strang time-splitting technique,we split the equation into linear part and nonlinear part.The linear part is solved with Fourier Pseudospectral method;the nonlinear part is solved analytically.We show that the method is easy to be applied and second-order in time and spectrally accurate in space.We apply the method to investigate soliton propagation,soliton interaction,and generation of stable moving pulses in one dimension and stable vortex solitons in two dimensions.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
基金the National Natural Science Foundation of China
文摘A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.
基金National Natural Science Foundation of China(No.11361037)。
文摘A numerical solution of a fractional-order reaction-diffusion model is discussed.With the development of fractional-order differential equations,Schnakenberg model becomes more and more important.However,there are few researches on numerical simulation of Schnakenberg model with spatial fractional order.It is also important to find a simple and effective numerical method.In this paper,the Schnakenberg model is numerically simulated by Fourier spectral method.The Fourier transform is applied to transforming the partial differential equation into ordinary differential equation in space,and the fourth order Runge-Kutta method is used to solve the ordinary differential equation to obtain the numerical solution from the perspective of time.Simulation results show the effectiveness of the proposed method.
文摘In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.
基金supported in part by the Ministry of Education of Singapore grant No.R-146-000-120-112the National Natural Science Foundation of China grant No.10901134.
文摘In this paper,we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation.Using the Strang time-splitting technique,we split the equation into linear part and nonlinear part.The linear part is solved with Fourier Pseudospectral method;the nonlinear part is solved analytically.We show that the method is easy to be applied and second-order in time and spectrally accurate in space.We apply the method to investigate soliton propagation,soliton interaction,and generation of stable moving pulses in one dimension and stable vortex solitons in two dimensions.
