Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915337171107840 |
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| author | Bakhvalov, Pavel |
| author_facet | Bakhvalov, Pavel |
| contents | Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular allows to construct implicit-explicit (IMEX) methods. Original SRK schemes (Colomes, Badia, IJNME, 2015) are designed for finite-element methods that satisfy the inf-sup condition. In this paper, the idea of SRK schemes is generalized to spatial discretizations with pressure stabilization. In the numerical experiments, SRK schemes are demonstrated with both finite-difference and finite element spatial discretizations. Numerical results show that one of the SRK schemes outperforms the third-order multistep projection-based method in terms of accuracy while preserving the computational costs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_09519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization Bakhvalov, Pavel Numerical Analysis 65M08, 65M60 G.1.8 Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular allows to construct implicit-explicit (IMEX) methods. Original SRK schemes (Colomes, Badia, IJNME, 2015) are designed for finite-element methods that satisfy the inf-sup condition. In this paper, the idea of SRK schemes is generalized to spatial discretizations with pressure stabilization. In the numerical experiments, SRK schemes are demonstrated with both finite-difference and finite element spatial discretizations. Numerical results show that one of the SRK schemes outperforms the third-order multistep projection-based method in terms of accuracy while preserving the computational costs. |
| title | Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization |
| topic | Numerical Analysis 65M08, 65M60 G.1.8 |
| url | https://arxiv.org/abs/2506.09519 |