An original integral formulation of the three-dimensional contravariant Navier-Stokes equations, devoid of the Christoffel symbols, in general time-dependent curvilinear coordinates is presented. The proposed integral form is obtained from the time derivative of the momentum of a material fluid volume and from the Leibniz rule of integration applied to a control volume that moves with a velocity which is different from the fluid velocity. The proposed integral formulation has general validity and makes it possible to obtain, with simple passages, the complete differential form of the contravariant Navier-Stokes equations in a time dependent curvilinear coordinate system. The integral form, devoid of the Christoffel symbols, proposed in this work is used in order to realise a three-dimensional non-hydrostatic numerical model for free surface flows, which is able to simulate the discontinuities in the solution related to the wave breaking on domains that reproduce the complex geometries of the coastal regions. The proposed model is validated by reproducing experimental test cases on time dependent curvilinear grids.

Integral contravariant form of the Navier-Stokes equations / Palleschi, Federica; Iele, Benedetta; Gallerano, Francesco. - In: WSEAS TRANSACTIONS ON FLUID MECHANICS. - ISSN 1790-5087. - 14:(2019), pp. 101-113.

Integral contravariant form of the Navier-Stokes equations

Palleschi, Federica
;
Iele, Benedetta;Gallerano, Francesco
2019

Abstract

An original integral formulation of the three-dimensional contravariant Navier-Stokes equations, devoid of the Christoffel symbols, in general time-dependent curvilinear coordinates is presented. The proposed integral form is obtained from the time derivative of the momentum of a material fluid volume and from the Leibniz rule of integration applied to a control volume that moves with a velocity which is different from the fluid velocity. The proposed integral formulation has general validity and makes it possible to obtain, with simple passages, the complete differential form of the contravariant Navier-Stokes equations in a time dependent curvilinear coordinate system. The integral form, devoid of the Christoffel symbols, proposed in this work is used in order to realise a three-dimensional non-hydrostatic numerical model for free surface flows, which is able to simulate the discontinuities in the solution related to the wave breaking on domains that reproduce the complex geometries of the coastal regions. The proposed model is validated by reproducing experimental test cases on time dependent curvilinear grids.
contravariant;iIntegral form; Navier-Stokes equations; shock-capturing scheme; three-dimensional; time-dependent curvilinear coordinate system
01 Pubblicazione su rivista::01a Articolo in rivista
Integral contravariant form of the Navier-Stokes equations / Palleschi, Federica; Iele, Benedetta; Gallerano, Francesco. - In: WSEAS TRANSACTIONS ON FLUID MECHANICS. - ISSN 1790-5087. - 14:(2019), pp. 101-113.
File allegati a questo prodotto
File Dimensione Formato  
Palleschi_Integral-contravariant-form_2019.pdf

accesso aperto

Note: http://wseas.org/wseas/cms.action?id=19933
Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 529.25 kB
Formato Adobe PDF
529.25 kB Adobe PDF Visualizza/Apri PDF

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/11573/1327601
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact