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EnglishWe propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the pressure-velocity coupling is fundamentally different, up to the point that the two approaches can be considered antithetical. The first method is kinetic energy preserving, meaning that the skew-symmetric discretization of the convective term is guaranteed not to alter the kinetic energy balance. The approximated velocity fields exactly satisfy the divergence free constraint and continuity of the normal component of the velocity is weakly enforced on the mesh skeleton, leading to H-div conformity. The second scheme relies on Godunov fluxes for pressure-velocity coupling: a Harten, Lax and van Leer approximated Riemann Solver designed for cell centered formulations is adapted to hybrid face centered formulations. The resulting numerical scheme is robust up to the inviscid limit, meaning that it can be applied for seeking approximate solutions of the incompressible Euler equations. The schemes are numerically validated performing steady and unsteady two dimensional test cases and evaluating the convergence rates on h-refined mesh sequences. In addition to standard benchmark flow problems, specifically conceived test cases are conducted for studying the error behaviour when approaching the inviscid limit.
(2022). HHO Methods for the Incompressible Navier-Stokes and the Incompressible Euler Equations [journal article - articolo]. In JOURNAL OF SCIENTIFIC COMPUTING. Retrieved from http://hdl.handle.net/10446/222848
| Citazione: | (2022). HHO Methods for the Incompressible Navier-Stokes and the Incompressible Euler Equations [journal article - articolo]. In JOURNAL OF SCIENTIFIC COMPUTING. Retrieved from http://hdl.handle.net/10446/222848 | |
| Titolo: | HHO Methods for the Incompressible Navier-Stokes and the Incompressible Euler Equations | |
| Tipologia specifica: | articolo | |
| Tutti gli autori: | Botti, Lorenzo Alessio; Massa, Francesco Carlo | |
| Numero degli autori: | 2 | |
| Autori unibg: | ||
| Contatti: | francescocarlo.massa@unibg.it | |
| Data di pubblicazione: | 2022 | |
| Lingua: | English | |
| URL: | https://www.springer.com/journal/10915 | |
| Rivista: | ||
| Referaggio: | esperti anonimi | |
| Vol.: | 92 | |
| Fascicolo: | 1 (art. 28) | |
| Pag. iniziale: | 1 | |
| Pag. finale: | 38 | |
| Supporto: | online | |
| DOI: | http://dx.doi.org/10.1007/s10915-022-01864-1 | |
| Settore Scientifico Disciplinare: | Settore ING-IND/06 - Fluidodinamica | |
| Keywords (eng): | Hybrid high-order; Navier–Stokes equations; Euler equations; Pressure-robust; Pointwise divergence free | |
| Abstract (eng): | We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and... investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the pressure-velocity coupling is fundamentally different, up to the point that the two approaches can be considered antithetical. The first method is kinetic energy preserving, meaning that the skew-symmetric discretization of the convective term is guaranteed not to alter the kinetic energy balance. The approximated velocity fields exactly satisfy the divergence free constraint and continuity of the normal component of the velocity is weakly enforced on the mesh skeleton, leading to H-div conformity. The second scheme relies on Godunov fluxes for pressure-velocity coupling: a Harten, Lax and van Leer approximated Riemann Solver designed for cell centered formulations is adapted to hybrid face centered formulations. The resulting numerical scheme is robust up to the inviscid limit, meaning that it can be applied for seeking approximate solutions of the incompressible Euler equations. The schemes are numerically validated performing steady and unsteady two dimensional test cases and evaluating the convergence rates on h-refined mesh sequences. In addition to standard benchmark flow problems, specifically conceived test cases are conducted for studying the error behaviour when approaching the inviscid limit. | |
| Altre informazioni: | indice consultabile alla pagina https://link.springer.com/journal/10915/volumes-and-issues/92-1 | |
| Data di archiviazione in Aisberg: | 2022-06-22T10:02:27Z | |
| Nelle collezioni: | 1.1.01 Articoli/Saggi in rivista - Journal Articles/Essays |
File allegato/i alla scheda:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| BOTTI, MASSA (2022) - HHO Methods for the Incompressible NS and Incompressible Euler equations.pdf | publisher's version - versione editoriale |  | Open AccessVisualizza/Apri |
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