A Fourier spectral scheme is proposed for solving the periodic problem of nonlinear Klein-Gordon equation. Its stability and convergence are investigated. Numerical results are also presented.
Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective met...Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.展开更多
A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which...A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which Fourier series of the film profile does not converge at jump points of groove start or groove end in the case of rectangle groove was still remained. In the paper, an inexpedience of numerical analysis under a special case at rectangle groove is challenged to solve. As a result, for compensation of which Fourier series does not converge at jump points in a special case of rectangle groove, Fourier coefficient of fluid film thickness is proposed as taking the limit of which in a case trapezoidal groove at trapezoidal angle approaches 0.展开更多
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-un...A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional explicit-implicit The treatment of equations. The third-order mixed scheme is employed the three-dimensional for time integration. non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.展开更多
文摘A Fourier spectral scheme is proposed for solving the periodic problem of nonlinear Klein-Gordon equation. Its stability and convergence are investigated. Numerical results are also presented.
基金This work is supported by the National Natural Science Foundations of Chinese under grant Nos, 10371118 and 90411009.
文摘Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.
文摘A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which Fourier series of the film profile does not converge at jump points of groove start or groove end in the case of rectangle groove was still remained. In the paper, an inexpedience of numerical analysis under a special case at rectangle groove is challenged to solve. As a result, for compensation of which Fourier series does not converge at jump points in a special case of rectangle groove, Fourier coefficient of fluid film thickness is proposed as taking the limit of which in a case trapezoidal groove at trapezoidal angle approaches 0.
基金Project supported by the National Natural Science Foundation of China (Grant No:10272040) and Doctor Foundation of Education Ministry (Grant No:20050294003)
文摘A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional explicit-implicit The treatment of equations. The third-order mixed scheme is employed the three-dimensional for time integration. non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
