The course will consist of three parts covering the physical nature of turbulence and a discussion and practice of numerical simulation.
Part I Physical Nature - Turbulence Origin in Boundary-Layer Flows, Predominant Mechanisms and Applications (Yury S. Kachanov)
2) What is turbulence? The problem of its definition and the solution of this problem.
3) Turbulence origin and its practical significance.
4) Transition scenarios and characteristic stages.
5) Classes and types of instability of laminar boundary layers.
6) Basic ideas of experimental approaches to the transition and turbulence researches.
7) Three bright examples of flow instabilities.
8) Boundary-layer receptivity to various external perturbations.
9) Three bright examples of the boundary-layer receptivity problems.
10) Nonlinear interactions of instability modes. Role of resonances.
11) Formation of vortical structures at late stages of turbulence origin and their universality.
12) Turbulence production mechanisms in transitional and turbulent flows and their similarity.
13) Deterministic turbulence Ė myth or reality?
14) Transition prediction approaches.
15) Control of boundary layer transition.
16) Control of turbulent boundary layers.
17) Concluding remarks.
Part II Direct Numerical Simulation for Flow Transition (Chaoqun Liu)
1) Governing equations of fluid motion
2) Detailed conservative Navier-Stokes equation in a curvilinear coordinate
3) Orthogonal body-fitted grid generation
4) High order compact scheme and filter
5) High order formula for boundary grid points
6) Runge-Kutta and implicit time marching
7) Universal high order subroutine for conservation and accurate numerical derivatives
8) MPI parallel computation
9) Numerical examples of flow transition
Part III DNS Code Practice (Chaoqun Liu)
Class seats are very limited and early registration is encouraged. For more information, please contact:
Prof. Chaoqun Liu
Department of Mathematics
456 PKH, 411 S. Nedderman, Box 19408
University of Texas at Arlington
Arlington, TX 76019-0408, USA
Web Link: http://www.uta.edu/math/courses/FTT09/