scholarly journals Error Analysis of a Subgrid Eddy Viscosity Multi-Scale Discretization of the Navier-Stokes Equations

SeMA Journal ◽  
2012 ◽  
Vol 60 (1) ◽  
pp. 51-74
Author(s):  
Christine Bernardi ◽  
Tomás Chacón Rebollo ◽  
Macarena Gómez Mármol
Keyword(s):  
Error Analysis ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multi Scale

scholarly journals On Error Analysis for the 3D Navier–Stokes Equations in Velocity-Vorticity-Helicity Form

2011 ◽  
Vol 49 (2) ◽  
pp. 711-732 ◽  
Author(s):  
Hyesuk K. Lee ◽  
Maxim A. Olshanskii ◽  
Leo G. Rebholz
Keyword(s):  
Error Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Spectral Galerkin Method in Space and Time for the 2Dg-Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Dao Trong Quyet
Keyword(s):  
Initial Data ◽  
Error Analysis ◽  
Galerkin Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Euler Scheme ◽  
Navier Stokes Equations ◽  
Space And Time ◽  
Spectral Galerkin Method

We prove theH2-stability andL2-error analysis of the spectral Galerkin method in space and time with the implicit/explicit Euler scheme for the 2Dg-Navier-Stokes equations in bounded domains when the initial data belong toH1.

Variational multi-scale finite element approximation of the compressible Navier-Stokes equations

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1240-1271 ◽  
Author(s):  
Camilo Andrés Bayona Roa ◽  
Joan Baiges ◽  
R Codina
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Shock Capturing ◽  
Navier Stokes ◽  
Element Approximation ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Multi Scale ◽  
Non Linear

Purpose – The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated. Design/methodology/approach – The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion. Findings – Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state. Originality/value – A complete investigation of the stabilized formulation of the compressible problem is addressed.

Conical turbulent swirling vortex with variable eddy viscosity

1986 ◽  
Vol 403 (1825) ◽  
pp. 235-268 ◽  
Keyword(s):  
Eddy Viscosity ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Vortex ◽  
The Core ◽  
Vortex Solutions ◽  
Variable Eddy Viscosity

In the one hundred years since Rankine suggested his well known two-dimensional vortex model with finite core, no one has ever found any exact vortex solutions of the Navier-Stokes equations that can satisfy a complete set of physical boundary conditions. In this paper a variable viscosity is introduced and the existence of conical turbulent vortex solutions of the Navier-Stokes equations is examined. It is found that for a class of deliberately chosen eddy viscosity function a steady turbulent vortex can, for the first time, satisfy both the regularity condition at the core and the adherence condition at the surface, except for a singularity at the origin inherent in all conical similarity solutions. In its asymptotic form, if the eddy viscosity only varies in a boundary layer near the surface or the core, outside the layer the solution given would approach one of the laminar solutions of Yih et al . ( Physics Fluids 25, 2147 (1982)) or that of Serrin ( Phil. Trans. R. Soc. Lond. A 271, 325 (1972)) respectively. These results reveal some remarkable relations between the behaviour, and even the existence, of a vortex and turbulence.

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