Differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical soluti...Differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical solutions of two_dimensional incompressible Navier_Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason, in this paper a combinative predicting_correcting numerical scheme for solving two_dimensional incompressible Navier_Stokes equations is presented by mixing upwind difference method into differential quadrature one. Using this scheme and pseudo_time_dependent algorithm, numerical solutions of high Reynolds number flow are obtained with only a few grid points. For example, 1∶1 and 1∶2 driven cavity flows are calculated and good numerical solutions are obtained.展开更多
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while t...A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.展开更多
A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three_dimensional incompressible Navier_Stokes ...A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three_dimensional incompressible Navier_Stokes equations. The transition from two_ to three_dimensional flow structures along the axial direction due to the vortical instability appears,and the three_dimensional structures lie alternatively on the two sides of the cylinder. Numerical study has been taken for the Keulegan_Carpenter(KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600. The force behaviors are also studied by solving the Morison equation. Calculated results agree well with experimental data and theoretical prediction.展开更多
The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and...The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and uniqueness of weak solution of this flow with the stream_velocity form, firstly, the relations among the nonlinear terms in this equation is found; then, the existence is proved by an auxiliary semi_discrete scheme and a compactness argument.展开更多
A kind simple postprocess procedure for classical Galerkin method for steady Navier_Stokes equations with stream function form was presented in this paper. The main ideal was to construct an approximate interactive ru...A kind simple postprocess procedure for classical Galerkin method for steady Navier_Stokes equations with stream function form was presented in this paper. The main ideal was to construct an approximate interactive rule between lower frequency components and higher frequency components by using the conception of Approximate Inertial Manifold(AIM) and a kind of new decomposition of the true solution. It is demonstrated in this paper that this kind of postprocess Galerkin method could derive a higher accuracy solution with lower computing efforts.展开更多
文摘Differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical solutions of two_dimensional incompressible Navier_Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason, in this paper a combinative predicting_correcting numerical scheme for solving two_dimensional incompressible Navier_Stokes equations is presented by mixing upwind difference method into differential quadrature one. Using this scheme and pseudo_time_dependent algorithm, numerical solutions of high Reynolds number flow are obtained with only a few grid points. For example, 1∶1 and 1∶2 driven cavity flows are calculated and good numerical solutions are obtained.
文摘A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
文摘A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three_dimensional incompressible Navier_Stokes equations. The transition from two_ to three_dimensional flow structures along the axial direction due to the vortical instability appears,and the three_dimensional structures lie alternatively on the two sides of the cylinder. Numerical study has been taken for the Keulegan_Carpenter(KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600. The force behaviors are also studied by solving the Morison equation. Calculated results agree well with experimental data and theoretical prediction.
文摘The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and uniqueness of weak solution of this flow with the stream_velocity form, firstly, the relations among the nonlinear terms in this equation is found; then, the existence is proved by an auxiliary semi_discrete scheme and a compactness argument.
文摘A kind simple postprocess procedure for classical Galerkin method for steady Navier_Stokes equations with stream function form was presented in this paper. The main ideal was to construct an approximate interactive rule between lower frequency components and higher frequency components by using the conception of Approximate Inertial Manifold(AIM) and a kind of new decomposition of the true solution. It is demonstrated in this paper that this kind of postprocess Galerkin method could derive a higher accuracy solution with lower computing efforts.
