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Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

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Abstract

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

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Authors and Affiliations

  1. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

    Huangxin Chen

  2. Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia

    Shuyu Sun & Tao Zhang

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  1. Huangxin Chen
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  2. Shuyu Sun
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Correspondence to Shuyu Sun.

Additional information

The work of Huangxin Chen was supported by the NSF of China (Grant Nos. 11771363, 91630204, 51661135011) and Program for Prominent Young Talents in Fujian Province University. Shuyu Sun acknowledges that this work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the Grant BAS/1/1351-01-01.

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Chen, H., Sun, S. & Zhang, T. Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids. J Sci Comput 75, 427–456 (2018). https://doi.org/10.1007/s10915-017-0543-3

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