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| Numerical study on stability and accuracy of the fractional step algorithm for the incompressible N-S equations |
| Revised:April 25, 2005 |
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| DOI：10.7511/jslx20073054 |
| KeyWord:incompressible N-S equation,u -p interpolation approximations,fractional step algorithm,Reynolds numbers,stability,accuracy |
| HAN Xian-hong LI Xi-kui |
| State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, Dalian 116023, China |
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| Abstract: |
| It is well known that the LBB stability condition precludes the use of elements with the equal low order of interpolation for velocity u and pressure p in the numerical modeling of the incompressible N-S equations.The fractional step algorithm based on the pressure Poisson equation was reported and well recognized to be capable of circumventing the restrictions imposed by the LBB condition.However,the recent work of Guermond indicates that the incremental version of the fractional step algorithm can hardly circumvent the LBB condition with success,and the non-incremental version may work well with equal-order interpolations only if the time step size is chosen to be sufficiently larger than a critical one.In the present paper a numerical study on stability and accuracy of the non-incremental and the incremental versions of the iterative fractional step algorithm is carried out with the plane Poiseuille flow problem under different Reynolds numbers.The results and conclusions obtained by the present study provide some references and instructions in proper use of the fractional step algorithm with a right choice of the u-p interpolation approximations. |
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