The Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in (Formula presented.). In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.

Weakly Compressible Approximation of the Taylor–Green Vortex Solution

Matteo Antuono
Primo
;
Salvatore Marrone
Ultimo
2025

Abstract

The Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in (Formula presented.). In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.
2025
Istituto di iNgegneria del Mare - INM (ex INSEAN)
analytical solutions
Taylor–Green vortex
weakly compressible flows
File in questo prodotto:
File Dimensione Formato  
Stud Appl Math - 2024 - Antuono - Weakly Compressible Approximation of the Taylor Green Vortex Solution.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 2.7 MB
Formato Adobe PDF
2.7 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/514488
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact