Numerical analysis of a corrected Smagorinsky model

@article{Siddiqua2022NumericalAO,
  title={Numerical analysis of a corrected Smagorinsky model},
  author={Farjana Siddiqua and Xihui Xie},
  journal={Numerical Methods for Partial Differential Equations},
  year={2022}
}
. The classical Smagorinsky model’s solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been corrected to incorporate this flow and still be well-posed. Herein we first develop some basic properties of the corrected model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 52 REFERENCES
Extension of a simplified Baldwin–Lomax model to nonequilibrium turbulence: Model, analysis and algorithms
Complex turbulence not at statistical equilibrium is impossible to simulate using eddy viscosity models due to a backscatter. This research presents the way to correct the Baldwin–Lomax model for
Rotational Forms of Large Eddy Simulation Turbulence Models: Modeling and Mathematical Theory
In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model, which is the extension of the Baldwin & Lomax model to non-equilibrium problems. The model is
Damping Functions correct over‐dissipation of the Smagorinsky Model
This paper studies the time‐averaged energy dissipation rate ⟨εSMD(u)⟩ for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over‐damp. One common
A Modified Smagorinsky Subgrid Scale Model for the Large Eddy Simulation of Turbulent Flow
TLDR
What a filter is and an issue related to filters are addressed; the error that results when the filtering and differential operations are interchanged is studied under the context of the Finite Element Method.
Error estimates for the Smagorinsky turbulence model: enhanced stability through scale separation and numerical stabilization
TLDR
In the presence of a spectral gap, such that the flow can be decomposed in a large scale with moderate gradient and a small amplitude fine scale with arbitratry gradient, the Smagorinsky model admits stability estimates for perturbations, with exponential growth depending only on the large scale gradient.
On the analysis of a geometrically selective turbulence model
Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider
Analysis of the K-epsilon turbulence model
The Navier-Stokes Equations. INCOMPRESSIBLE FLUIDS. Homogeneous Incompressible Turbulence. Reynolds Hypothesis. The k-epsis Model. Mathematical Analysis and Approximation. Other Models Beyond k-epsis
How conservative?
...
...