## Abstract

Pressure Poisson equation (PPE) reformulations of the incompressible Navier–Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a time-evolution equation for the velocity field only, with the pressure gradient acting as a nonlocal operator. Thus, numerical methods based on PPE reformulations are representatives of a class of methods that have no principal limitations in achieving high order. In this paper, it is studied to what extent high-order methods for the NSE can be obtained from a specific PPE reformulation with electric boundary conditions (EBC). To that end, implicit–explicit (IMEX) time-stepping is used to decouple the pressure solve from the velocity update, while avoiding a parabolic time-step restriction; and mixed finite elements are used in space, to capture the structure imposed by the EBC. Via numerical examples, it is demonstrated that the methodology can yield at least third order accuracy in space and time.

Original language | English (US) |
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Article number | 113451 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 373 |

DOIs | |

State | Published - Jan 1 2021 |

## All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications

## Keywords

- Electric boundary conditions
- IMEX schemes
- Incompressible Navier–Stokes
- Mixed finite elements
- Pressure Poisson equation