A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations |
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Authors: | Yuxin Ren Yuxi Jiang Miao''er Liu Hanxin Zhang |
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Affiliation: | (1) Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China;(2) CNOOC Research Center, Beijing, China;(3) National Key Laboratory for CFD, Beijing, China |
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Abstract: | In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the local- truncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases. The project supported by the China NKBRSF (2001CB409604) The English text was polished by Yunming Chen |
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Keywords: | Incompressible Navier-Stokes equations Projection methods Third-order scheme Local truncation error |
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