Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability.
Bibliographical noteFunding Information:
Acknowledgements This paper is based on part of Yuki Saka’s Ph.D. dissertation written under the direction of MDG and XW. This work is supported in part by the grants from the Air Force Office of Scientific Research FA9550-08-1-0415 (MG and EL) and FA9550-09-1-0058 (CT) and the National Science Foundation DMS-0606671 (XW).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Numerical Analysis
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics