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Presure Boundary Conditions in the Collocated Finite-Volume Method for the Steady Navier–Stokes Equations

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Abstract

The pressure boundary conditions for the steady-state solution of the incompressible Navier–Stokes equations with the collocated finite-volume method are discussed. This work is based on inf-sup stable coupled flux approximation. The flux is derived based on the linearity assumption of the velocity and pressure unknowns that yields one-sided flux expressions. Enforcing continuity of these expressions on internal interface we reconstruct the interface velocity and pressure and obtain single continuous flux. As a result, the conservation for the momentum and the divergence is discretely exact. However, on boundary interfaces additional pressure boundary condition is required to reconstruct the interface pressure.

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Funding

This work was supported by the Russian Science Foundation through the grant 19-71-10094.

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  1. Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia

    K. M. Terekhov

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    K. M. Terekhov

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  1. K. M. Terekhov
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Correspondence to K. M. Terekhov.

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Terekhov, K.M. Presure Boundary Conditions in the Collocated Finite-Volume Method for the Steady Navier–Stokes Equations. Comput. Math. and Math. Phys. 62, 1345–1355 (2022). https://doi.org/10.1134/S0965542522080139

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  • DOI: https://doi.org/10.1134/S0965542522080139

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