scholarly journals Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations

2020 ◽  
Author(s):  
Franco Flandoli ◽  
Lucio Galeati ◽  
Dejun Luo
Keyword(s):  
Euler Equations ◽  
Stokes Equations ◽  
Scaling Limit ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
2D Euler Equations

scholarly journals Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit

2021 ◽  
Vol 240 (1) ◽  
pp. 295-326
Author(s):  
Gennaro Ciampa ◽  
Gianluca Crippa ◽  
Stefano Spirito
Keyword(s):  
Euler Equations ◽  
Stokes Equations ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Lagrangian Solution ◽  
Viscosity Limit ◽  
2D Euler Equations

AbstractIn this paper we prove the uniform-in-time $$L^p$$ L p convergence in the inviscid limit of a family $$\omega ^\nu $$ ω ν of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution $$\omega $$ ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $$\omega ^{\nu }$$ ω ν to $$\omega $$ ω in $$L^p$$ L p . Finally, we show that solutions of the Euler equations with $$L^p$$ L p vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.

Uniqueness of the exact solutions of the Navier—Stokes equations having null nonlinearity

2006 ◽  
Vol 136 (6) ◽  
pp. 1303-1315 ◽  
Author(s):  
Sun-Chul Kim ◽  
Hisashi Okamoto
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Euler Equations ◽  
Stokes Equations ◽  
Elliptic Partial Differential Equations ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Overdetermined System ◽  
Navier Stokes Equations

We consider an overdetermined system of elliptic partial differential equations arising in the Navier–Stokes equations. This analysis enables us to prove that the well-known classical solutions such as Couette flows and others are the only solutions that satisfy both the stationary Navier–Stokes and Euler equations.

scholarly journals Embedded direct numerical simulation for aeronautical CFD

2001 ◽  
Vol 105 (1046) ◽  
pp. 193-198 ◽  
Author(s):  
N. D. Sandham ◽  
M. Alam ◽  
S. Morin
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Euler Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Modified Equations ◽  
Separation Bubbles

Abstract A method is proposed by which a direct numerical simulation of the compressible Navier-Stokes equations may be embedded within a more general aeronautical CFD code. The method may be applied to any code which solves the Euler equations or the Favre-averaged Navier-Stokes equations. A formal decomposition of the flowfield is used to derive modified equations for use with direct numerical simulation solvers. Some preliminary applications for model flows with transitional separation bubbles are given.

Viscous profiles of vortex patches

2013 ◽  
Vol 14 (1) ◽  
pp. 1-68 ◽  
Author(s):  
Franck Sueur
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Euler Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
Sharp Variation

AbstractWe deal with the incompressible Navier–Stokes equations with vortex patches as initial data. Such data describe an initial configuration for which the vorticity is discontinuous across a hypersurface. We give an asymptotic expansion of the solutions in the vanishing viscosity limit which exhibits an internal layer where the fluid vorticity has a sharp variation. This layer moves with the flow of the Euler equations.

scholarly journals Derivation of a Viscous Serre–Green–Naghdi Equation: An Impasse?

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 135
Author(s):  
Denys Dutykh ◽  
Hervé V.J. Le Meur
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Euler Equations ◽  
Stokes Equations ◽  
Current Status ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Bottom Region ◽  
Flow Domain ◽  
Layer Flow

In this article, we present the current status of the derivation of a viscous Serre–Green–Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier–Stokes equations. We consider a particular regime binding the Reynolds number and the shallowness parameter. The computations presented in this article are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prandtl-like equation that we claim to be irreducible. Further approximations are necessary to obtain a tractable model.

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