Abstract
Based on the artificial compressible method, an iteration penalty semi-discrete scheme is proposed for the numerical simulations of the incompressible Navier-Stokes equations with variable density. Compared with the classical penalty scheme, the main feature is that the proposed iteration penalty scheme is of the first-order temporal convergence rate for any penalty parameter ε > 0 independent of the time step size τ. Numerical results are given to illustrate the theoretical analysis.
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Funding
This work was supported by the 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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Communicated by: Long Chen
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An, R. Iteration penalty method for the incompressible Navier-Stokes equations with variable density based on the artificial compressible method. Adv Comput Math 46, 5 (2020). https://doi.org/10.1007/s10444-020-09757-3
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DOI: https://doi.org/10.1007/s10444-020-09757-3
Keywords
- Variable density incompressible flows
- Navier-Stokes equations
- Iteration penalty method
- Stability
- Error estimates