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

TL;DR

This paper extends Segregated Runge-Kutta schemes to pressure-stabilized spatial discretizations for the incompressible Navier-Stokes equations, demonstrating improved accuracy over existing methods while maintaining similar computational costs.

Contribution

It generalizes SRK schemes to pressure-stabilized discretizations and validates their effectiveness with finite-difference and finite element methods.

Findings

SRK schemes outperform third-order multistep methods in accuracy

Numerical results confirm effectiveness with different spatial discretizations

Computational costs are preserved compared to existing methods

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.