High-order finite element methods for a pressure Poisson equation reformulation of the Navier–Stokes equations with electric boundary conditions
Document Type
Article
Publication Date
1-1-2021
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.
Identifier
85094322362 (Scopus)
Publication Title
Computer Methods in Applied Mechanics and Engineering
External Full Text Location
https://doi.org/10.1016/j.cma.2020.113451
ISSN
00457825
Volume
373
Grant
1625061
Fund Ref
National Science Foundation
Recommended Citation
Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; and Zhou, Dong, "High-order finite element methods for a pressure Poisson equation reformulation of the Navier–Stokes equations with electric boundary conditions" (2021). Faculty Publications. 4660.
https://digitalcommons.njit.edu/fac_pubs/4660
