Explicit-Iterative Scheme for the Time Integration of a System of Navier–Stokes Equations

We propose a new explicit-iterative scheme for time integrating the multidimensional Navier–Stokes equations of a compressible environment through splitting into convective and diffusive stages, which are performed sequentially at each time step. The convective stage is implemented using the Godunov...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2020-11, Vol.12 (6), p.958-968
Main Authors: Zhukov, V. T., Feodoritova, O. B., Novikova, N. D., Duben, A. P.
Format: Article
Language:English
Subjects:
Chebyshev approximation
Compressibility
Conservation laws
Fluid dynamics
Fluid flow
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Simulation and Modeling
Time integration
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Summary:We propose a new explicit-iterative scheme for time integrating the multidimensional Navier–Stokes equations of a compressible environment through splitting into convective and diffusive stages, which are performed sequentially at each time step. The convective stage is implemented using the Godunov scheme; and the diffusive stage, using the Chebyshev explicit-iterative LI-M scheme, which has no restriction on the time step. The resulting scheme ensures that the basic conservation laws hold on arbitrary irregular grids. The explicit nature of the calculations ensures that the scheme can be efficiently used in various parallel technologies.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048220060174