Fast-Projection Methods for the Incompressible Navier–Stokes Equations
An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/5/4/222 |
| _version_ | 1797546348066635776 |
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| author | Carlo De Michele Francesco Capuano Gennaro Coppola |
| author_facet | Carlo De Michele Francesco Capuano Gennaro Coppola |
| author_sort | Carlo De Michele |
| collection | DOAJ |
| description | An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations. |
| first_indexed | 2024-03-10T14:28:33Z |
| format | Article |
| id | doaj.art-d53cfa4ea8b7497fbd4b6219d6bf9a03 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T14:28:33Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-d53cfa4ea8b7497fbd4b6219d6bf9a032023-11-20T22:48:51ZengMDPI AGFluids2311-55212020-11-015422210.3390/fluids5040222Fast-Projection Methods for the Incompressible Navier–Stokes EquationsCarlo De Michele0Francesco Capuano1Gennaro Coppola2Dipartimento di Ingegneria Industriale (DII), Università di Napoli “Federico II”, 80125 Napoli, ItalyDipartimento di Ingegneria Industriale (DII), Università di Napoli “Federico II”, 80125 Napoli, ItalyDipartimento di Ingegneria Industriale (DII), Università di Napoli “Federico II”, 80125 Napoli, ItalyAn analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations.https://www.mdpi.com/2311-5521/5/4/222computational fluid dynamicsincompressible flowsprojection methods |
| spellingShingle | Carlo De Michele Francesco Capuano Gennaro Coppola Fast-Projection Methods for the Incompressible Navier–Stokes Equations Fluids computational fluid dynamics incompressible flows projection methods |
| title | Fast-Projection Methods for the Incompressible Navier–Stokes Equations |
| title_full | Fast-Projection Methods for the Incompressible Navier–Stokes Equations |
| title_fullStr | Fast-Projection Methods for the Incompressible Navier–Stokes Equations |
| title_full_unstemmed | Fast-Projection Methods for the Incompressible Navier–Stokes Equations |
| title_short | Fast-Projection Methods for the Incompressible Navier–Stokes Equations |
| title_sort | fast projection methods for the incompressible navier stokes equations |
| topic | computational fluid dynamics incompressible flows projection methods |
| url | https://www.mdpi.com/2311-5521/5/4/222 |
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