Mathematical and Numerical Foundations of Turbulence Models and Applications

This monograph provides a detailed look at eddy viscosity models from theoretical and numerical angles. In particular, it gives a rigorous derivation of these models and shows through careful analysis how they can be applied to oceanic and atmospheric flows.

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science.Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows.Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

Draws on the most current, cutting-edge research in the field Encompasses complementary numerical and theoretical aspects of fluid dynamics Compiles related information that cannot be found together in any other place Contains many lesser-known but useful mathematical and numerical tools Valuable as both a reference resource and as a graduate text Includes supplementary material: sn.pub/extras

Autorentext

The author is a professor at XX University.

Inhalt

Introduction.- Incompressible Navier-Stokes Equations.- Mathematical Basis of Turbulence Modeling.- The k Model.- Laws of the Turbulence by Similarity Principles.- Steady Navier-Stokes Equations with Wall Laws and Fixed Eddy Viscosities.- Analysis of the Continuous Steady NS-TKE Model.- Evolutionary NS-TKE Model.- Finite Element Approximation of Steady Smagorinsky Model.- Finite Element Approximation of Evolution Smagorinsky Model.- A Projection-based Variational Multi-Scale Model.- Numerical Approximation of NS-TKE Model.- Numerical Experiments.- Appendix A: Tool Box.