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Characteristic-based operator-splitting finite element method for Navier-Stokes equations

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Abstract

A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly. The driven square flow and backward-facing step flow are conducted to validate the model. It is shown that the numerical results agree well with the standard solutions or existing experimental data, and the present model has high accuracy and good stability. It provides a prospective research method for solving N-S equations.

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Authors and Affiliations

  1. Research Center for Numerical Tests on Material Failure, Dalian University, Dalian, 116622, China

    DaGuo Wang & HaiJiao Wang

  2. Department of Information Engineering, Dalian University, Dalian, 116622, China

    HaiJiao Wang

  3. Department of Underground Construction and Engineering, Tongji University, Shanghai, 200092, China

    JuHua Xiong

  4. Department of Civil and Structural Engineering, The University of Hong Kong, Hong Kong, 999077, China

    L. G. Tham

Authors
  1. DaGuo Wang
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  2. HaiJiao Wang
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  3. JuHua Xiong
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  4. L. G. Tham
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Correspondence to DaGuo Wang.

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Wang, D., Wang, H., Xiong, J. et al. Characteristic-based operator-splitting finite element method for Navier-Stokes equations. Sci. China Technol. Sci. 54, 2157–2166 (2011). https://doi.org/10.1007/s11431-011-4444-7

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  • DOI: https://doi.org/10.1007/s11431-011-4444-7

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