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arXiv · 2506.09519

Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization

Pavel Bakhvalov
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Abstract

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.

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Pavel Bakhvalov. 2025-06-11. Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization. https://arxiv.org/abs/2506.09519

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