High-order time stepping for the Navier-Stokes equations with minimal computational complexity

TL;DR

This paper introduces high-order time-stepping schemes for the Navier-Stokes equations that decouple velocity components, simplifying the solution process to independent parabolic problems and explicitly recovering pressure.

Contribution

The paper extends existing schemes to achieve decoupling of velocity components, reducing computational complexity for solving incompressible Navier-Stokes equations.

Findings

Decoupling velocity components simplifies computations.

Pressure can be explicitly recovered after velocity computation.

The schemes are efficient for high-order time integration.

Abstract

In this paper we present extensions of the schemes proposed in \cite{GM14} that lead to a decoupling of the velocity components in the momentum equation. The new schemes reduce the solution of the incompressible Navier-Stokes equations to a set of classical uncoupled parabolic problems for each Cartesian component of the velocity. The pressure is explicitly recovered after the velocity is computed.