A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedrons circumcentres. In 3D problems, non-Delaunay meshes are provided by most of the mesh generators. To maintain good matrix properties for non-Delaunay meshes, a continuity equation is integrated over each tetrahedron, but the momentum equations are integrated over clusters of tetrahedrons, such that each external face shared by two clusters belongs to two tetrahedrons whose circumcentres have positive distance. A numerical procedure is proposed to compute the velocities inside clusters with more than one tetrahedron. Model preserves mass balance at the machine error and there is no need to compute pressure at each time iteration, but only at target simulation times.

costanza aricò, calogero picone, marco sinagra, & tullio tucciarelli (2021). MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case. In MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case.

MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case

costanza aricò;calogero picone;marco sinagra;tullio tucciarelli
2021

Abstract

A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedrons circumcentres. In 3D problems, non-Delaunay meshes are provided by most of the mesh generators. To maintain good matrix properties for non-Delaunay meshes, a continuity equation is integrated over each tetrahedron, but the momentum equations are integrated over clusters of tetrahedrons, such that each external face shared by two clusters belongs to two tetrahedrons whose circumcentres have positive distance. A numerical procedure is proposed to compute the velocities inside clusters with more than one tetrahedron. Model preserves mass balance at the machine error and there is no need to compute pressure at each time iteration, but only at target simulation times.
A new numerical solver for the 3D Navier Stokes incompressible laminar problems is proposed; The proposed model is suitable for the solution of laminar flows in irregular domains
costanza aricò, calogero picone, marco sinagra, & tullio tucciarelli (2021). MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case. In MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case.
File in questo prodotto:
File Dimensione Formato  
IAHR_2020_book_of_abstracts_final_only_MAST.pdf

non disponibili

Tipologia: Versione Editoriale
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/10447/548802
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact