A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces

We develop a novel Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces. The key ingredients of the method are discrete versions of the body force and convective contributions in the momentum equation formulated in terms of a globally diverg...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2020-05, Vol.79 (9), p.2655-2677
Main Authors: Castanon Quiroz, Daniel, Di Pietro, Daniele A.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Convergence
Divergence
Fluid flow
Fluid mechanics
Formulations
Hybrid High-Order methods
Incompressible Navier–Stokes equations
Mathematics
Mechanics
Navier-Stokes equations
Numerical Analysis
Physics
Robust a priori error estimates
Robustness (mathematics)
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Summary:We develop a novel Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces. The key ingredients of the method are discrete versions of the body force and convective contributions in the momentum equation formulated in terms of a globally divergence-free velocity reconstruction. Two key properties are mimicked at the discrete level, namely the invariance of the velocity with respect to irrotational body forces and the non-dissipativity of the convective term. A full convergence analysis is carried out, showing optimal orders of convergence under a smallness condition involving only the solenoidal part of the body force. The performance of the method is illustrated by a complete panel of numerical tests, including comparisons that highlight the benefits with respect to more standard formulations.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.12.005