Error Analysis of a New Fractional-Step Method for the Incompressible Navier–Stokes Equations with Variable Density

Abstract

A new fractional-step scheme for the numerical solution to the incompressible Navier–Stokes equations with variable density is proposed. Compared with other known methods, the numerical velocity and pressure are determined by a generalized Stokes problem per time step. The stability and convergence rate \(\mathcal O(\tau )\) of the scheme are proved and the performance of the scheme is numerically illustrated.

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Acknowledgements

This work was supported by National Natural Science Foundation of China with Grant No. 11771337 and by Zhejiang Provincial Natural Science Foundation with Grant Nos. LY18A010021 and LY16A010017.

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Correspondence to Rong An.

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An, R. Error Analysis of a New Fractional-Step Method for the Incompressible Navier–Stokes Equations with Variable Density. J Sci Comput 84, 3 (2020). https://doi.org/10.1007/s10915-020-01253-6

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Keywords

  • Variable density flows
  • Navier–Stokes equations
  • Fractional-step method
  • Stability
  • Convergence rate

Mathematics Subject Classification

  • 65N30
  • 76M05