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| Spectral element method and high order time splitting method for navies stokes equation |
| Revised:June 19, 2000 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20023061 |
| KeyWord:spectral element method,time splitting method,navier stokes equation |
| Chen Xuejiang Qin Guoliang Xu Zhong |
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| Abstract: |
| The calculational formula of the spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is induced in detail in this paper. The spectral element method is a high order weighted residual technique. In this method, firstly, the computational domain is broken into a series of elements, and the variable such as the velocity and the pressure is represented as a high order interpolation polynomial through Chebyshev collocation points, and then the element matrix is formed by finite element method. Lastly, the system matrix is constructed by element stiffness matrix summation, and the answer is obtained by solving the linear equation set. A formulation for splitting methods is also developed that results in high order time accurate schemes for the solution of incompressible Navier Stokes equations. The normal time splitting method is improved by applying third order explicit Adams Bashforth method and fourth order Runge Kutta method to the nonlinear connective terms, and third order implicit Adams Molten method to the linear terms. And the third order pressure boundary conditions for Possion equation for the pressure is employed as well. Using the high order time splitting method and high order pressure boundary conditions, the precision of the time discretization is advanced, and we can calculate the flow by longer time step to improve the efficiency of calculation. The advance of the precision for the time discretization is also useful for high Re fluid calculation. Then the high order time splitting method to split the incompressible Navier Stokes Equation, combining with the spectral element method, is utilized to simulate one typical sample in computational fluid dynamics, lid driven flow in closed square cavity. In the case of the same calculational accuracy and the same grid, the paper increase the Reynolds number from Re=100 that can be obtained using the normal time splitting method and the spectral element method to Re=600, and the time of convergence is shortened by using longer time step. The results show desirable agreement with the accepted benchmark solutions. Lastly, the changes of the field of velocity are analyzed according to different Reynolds Numbers. The validity of methods for fluid flow in this paper is proved. |
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