The present contribution constitutes an introduction and a survey of the "divergence-free" Virtual Element Method (VEM) for the Stokes and Navier-Stokes equations. It is a survey since it reviews all the main concepts regarding this kind of Virtual Elements and it is an introduction since it is written, both in terms of presentation and details, in order to be easily readable for newcomers. In particular we show the construction of the divergence-free virtual element velocity space for the Stokes equation and its enhanced version for the Navier-Stokes equation, and the explicit computation of the projection operators. We exhibit both the 2D (straight and curved polygons) and the 3D case. Furthermore we explore the main features and the advantages of the "divergence -free" construction. We believe the present paper constitutes a good reading for researchers that have some minimal knowledge of virtual elements and want to understand the "divergence-free" VEM approach for fluid mechanics.
An Introduction to Second Order Divergence-Free VEM for Fluidodynamics
Vacca G.
2022-01-01
Abstract
The present contribution constitutes an introduction and a survey of the "divergence-free" Virtual Element Method (VEM) for the Stokes and Navier-Stokes equations. It is a survey since it reviews all the main concepts regarding this kind of Virtual Elements and it is an introduction since it is written, both in terms of presentation and details, in order to be easily readable for newcomers. In particular we show the construction of the divergence-free virtual element velocity space for the Stokes equation and its enhanced version for the Navier-Stokes equation, and the explicit computation of the projection operators. We exhibit both the 2D (straight and curved polygons) and the 3D case. Furthermore we explore the main features and the advantages of the "divergence -free" construction. We believe the present paper constitutes a good reading for researchers that have some minimal knowledge of virtual elements and want to understand the "divergence-free" VEM approach for fluid mechanics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
