Search results for "Navier Stokes"

MAST-RT0 SOLUTION OF 3D NAVIER STOKES EQUATIONS ON UNSTRUCTURED MESHS. PRELIMINARY RESULTS IN THE LAMINAR CASE

2021

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

2021

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 tetrahedr…

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

2013

Abstract We compute the solutions of Prandtl’s and Navier–Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl’s equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier–Stokes solution at different Reynolds numbers Re = 103–105, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers Re = 104–105. We also investi…

On the convergence of a finite volume method for the Navier–Stokes–Fourier system

2020

Abstract The goal of the paper is to study the convergence of finite volume approximations of the Navier–Stokes–Fourier system describing the motion of compressible, viscous and heat-conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order $\mathcal O(h^{ \varepsilon +1})$, $0<\varepsilon <1$. The approximate solutions are piecewise constant functions with respect to the underlying polygonal mesh. We show that the numerical solutions converge strongly to the classical solution as long as the latter exists. On the other hand, any uniformly bounded sequence of numerical solutions converges unconditionally to the classical solution of t…

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex array

2008

Numerical solutions of Prandtl’s equation and Navier Stokes equations are considered for the two dimensional flow induced by an array of periodic rec- tilinear vortices interacting with an infinite plane. We show how this initial datum develops a separation singularity for Prandtl equation. We investigate the asymptotic validity of boundary layer theory considering numerical solu- tions for the full Navier Stokes equations at high Reynolds numbers.

LATTICE–BOLTZMANN SIMULATION OF DENSE NANOFLOWS: A COMPARISON WITH MOLECULAR DYNAMICS AND NAVIER–STOKES SOLUTIONS

2007

In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nano…

Transition to turbulence and Singularity in Boundary Layer Theory

2007

We compute the solutions of Prandtl’s and Navier- Stokes equations for the two dimensional flow induced by an array of periodic rectilinear vortices interacting with a boundary in the halfplane. This initial datum develops, in a finite time, a separation singularity for Prandtl’s equation. We investigate the different stages of unsteady separation in Navier-Stokes solutions for various Reynolds numbers. We show the presence of a large- scale interaction between viscous boundary layer and inviscid outer flow in all Re regimes, while the presence of a small-scale interaction is visible only for moderate-high Re numbers. We also investigate the asymptotic validity of boundary layer theory in t…

INSTABILITY OF HAMILTONIAN SYSTEMS IN THE SENSE OF CHIRIKOV AND BIFURCATION IN A NON LINEAR EVOLUTION PROBLEM EMANATING FROM PHYSICS

2004

We prove the existence of a minimal geometrico-dynamical condition to create hyperbolicity in section in the vicinity of a transversal homoclinic partially hyperbolic torus in a near integrable Hamiltonian system with three degrees of freedom. We deduce in this context a generalization of the Easton's theorem of symbolic dynamics. Then we give the optimal estimation of the Arnold diffusion time along a transition chain in the initially hyperbolic Hamiltonian systems with three degrees of freedom with a surrounding chain of hyperbolic periodic orbits .In a second part, we describe geometrically a mechanism of diffusion studied by Chirikov in a near integrable Hamiltonian system with three de…