Piero Bassanini

Unsteady Viscous Flows about Bodies: Vorticity Release and Forces

The force (drag and lift) exerted on a body moving in a viscous fluid is expressed via the ‘free’ and ‘bound’ vorticity moments, and the role of vortex shedding is discussed. The formulation encompasses classical, inviscid flows, and leads to efficient computational methods. Numerical results for a few prototype flows are presented.

On the Removal of the Trailing Edge Singularity in 3D Flows

The steady incompressible inviscid flow past a 3D airfoil with a sharp trailing edge TE is not uniquely determined by the free stream velocity U, unless some information about the shed vorticity is added. Namely, the concentrated vorticity ω normal to TE, which forms the vortex sheet released from the airfoil in steady state conditions, is an extra unknown to be determined by the solution. In fact, the irrotational flow is unique, contrary to what happens in 2D, but the real flow including the wake is not, and a Kutta condition is needed in order to determine ω and to retrieve uniqueness.

Free streamline-boundary layer analysis for separated flow over an airfoil

We propose a model which combines boundary layer computations with a free streamline potential flow for obtaining pressure distributions on an airfoil section in steady flow near stall conditions. The model is conceptually simple and uses elements which can be computed rapidly and efficiently. The solution is essentially analytical and can be used naturally in the larger context of matching asymptotic expansions to get information about three dimensional flows.SommarioSi propone un metodo di calcolo della pressione lungo un profile alare in regime di flusso stazionario in prossimitã dello stallo. II metodo combina le equazioni dello strato limite con un modello di flusso a linee di corrente libere e scia separata. I risultati numerici richiedono un minimo dispendio di tempo di calcolo e sono in buon accordo con gli esperimenti e con una soluzione viscosa.

Elliptic Partial Differential Equations of Second Order

We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations of second order. A linear partial differential operator L defined by

Distributions and Sobolev Spaces

Lu{\text{: = }}{a_{ij}}\left( x \right){D_{ij}}u + {b_i}\left( x \right){D_i}u + c\left( x \right)u

Hyperbolic Systems of Conservation Laws in One Space Variable

is elliptic on Ω ⊂ ℝ n if the symmetric matrix [a ij ] is positive definite for each x ∈ Ω. We have used the notation D i u, D ij u for partial derivatives with respect to x i and x i , x j and the summation convention on repeated indices is used. A nonlinear operator Q,

Theory and applications of partial differential equations

Q\left( u \right): = {a_{ij}}\left( {x,u,Du} \right){D_{ij}}u + b\left( {x,u,Du} \right)