@Article{IJNAM-10-4,
author = {Shan, L. and W., Layton, J. and Zheng, H.},
title = {Numerical Analysis of Modular VMS Methods with Nonlinear Eddy Viscosity for the Navier-Stokes Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {4},
pages = {943--971},
abstract = {<p style="text-align: justify;">This paper presents the stabilities for both two modular, projection-based variational multiscale (VMS) methods and the error analysis for only first one for the incompressible Navier-Stokes equations, extending the analysis in [39] to include nonlinear eddy viscosities. In VMS
methods, the influence of the unresolved scales onto the resolved small scales is modeled by a
Smagorinsky-type turbulent viscosity acting only on the marginally resolved scales. Different realization
of VMS models arise through different models of fluctuations. We analyze a method
of inducing a VMS treatment of turbulence in an existing NSE discretization through an additional,
uncoupled projection step. We prove stability, identifying the VMS model and numerical
dissipation and give an error estimate. Numerical tests are given that confirm and illustrate the
theoretical estimates. One method uses a fully nonlinear step inducing the VMS discretization.
The second induces a nonlinear eddy viscosity model with a linear solve of much less cost.</p>},
issn = {2617-8710},
doi = {https://doi.org/2013-IJNAM-605},
url = {https://global-sci.com/article/83445/numerical-analysis-of-modular-vms-methods-with-nonlinear-eddy-viscosity-for-the-navier-stokes-equations}
}