A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for s...A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.展开更多
To account for effects of nonlinearty on the wave-propagationcharacteristics, by using Green's second i-dentity a nonlinear consistent equation for water wavespropagating over arbitrary depths is derived by introd...To account for effects of nonlinearty on the wave-propagationcharacteristics, by using Green's second i-dentity a nonlinear consistent equation for water wavespropagating over arbitrary depths is derived by introducing a function as approximation to the exactvelocity protential function for the nonlinear governing equations, which can be simplified to tehlinear uniform mild-slope equation given by Zhang and Edge recently. In shallow water the equationreduces to a nonlinear equation of Boussinesq-type. In deep water the nonlinear dispersion relationfor Stokes expansion is found.展开更多
For the second-order charachteristics schemes of hyperbolic convection e-quations, an analysis of the occurring factors of overshoots and undershoots is made, and the nonoscillatory conditions are found. Either the La...For the second-order charachteristics schemes of hyperbolic convection e-quations, an analysis of the occurring factors of overshoots and undershoots is made, and the nonoscillatory conditions are found. Either the Lax-Wendroff scheme or the second-order upwind scheme is employed according to the value of the smooth parameter rj+-1/2 of the slope ratio of the solution. Numerical results show that the oscillation can be avoided and the high-order accuracy can be preserved. It is verified by a lot of numerical tests on typical examples of scalar convection equations. Further study is required for its extension to the system of hyperbolic equations.展开更多
文摘A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.
文摘To account for effects of nonlinearty on the wave-propagationcharacteristics, by using Green's second i-dentity a nonlinear consistent equation for water wavespropagating over arbitrary depths is derived by introducing a function as approximation to the exactvelocity protential function for the nonlinear governing equations, which can be simplified to tehlinear uniform mild-slope equation given by Zhang and Edge recently. In shallow water the equationreduces to a nonlinear equation of Boussinesq-type. In deep water the nonlinear dispersion relationfor Stokes expansion is found.
文摘For the second-order charachteristics schemes of hyperbolic convection e-quations, an analysis of the occurring factors of overshoots and undershoots is made, and the nonoscillatory conditions are found. Either the Lax-Wendroff scheme or the second-order upwind scheme is employed according to the value of the smooth parameter rj+-1/2 of the slope ratio of the solution. Numerical results show that the oscillation can be avoided and the high-order accuracy can be preserved. It is verified by a lot of numerical tests on typical examples of scalar convection equations. Further study is required for its extension to the system of hyperbolic equations.
