A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations - Archive ouverte HAL Access content directly
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2024

A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations

Jia Jia Qian
  • Function : Author
  • PersonId : 1331983

Abstract

In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using serendipity techniques. The main features of the DDR approach are the support of general meshes and arbitrary approximation orders. The method we develop is based on the curl-curl formulation of the momentum equation and, through compatibility with the Helmholtz-Hodge decomposition, delivers pressure-robust error estimates for the velocity. It also enables non-standard boundary conditions, such as imposing the value of the pressure on the boundary. In-depth numerical validation on a complete panel of tests including general polyhedral meshes is provided. The paper also contains an appendix where bounds on DDR potential reconstructions and differential operators are proved in the more general framework of Polytopal Exterior Calculus.
Fichier principal
Vignette du fichier
ns-ddr-hal.pdf (769.88 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Licence : CC BY NC - Attribution - NonCommercial

Dates and versions

hal-04375767 , version 1 (05-01-2024)

Licence

Attribution - NonCommercial

Identifiers

Cite

Daniele A. Di Pietro, Jérôme Droniou, Jia Jia Qian. A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 2024, 421, pp.116765. ⟨10.1016/j.cma.2024.116765⟩. ⟨hal-04375767⟩
16 View
9 Download

Altmetric

Share

Gmail Facebook X LinkedIn More