UTA Department of Mathematics


Home > New Course Offerings > Flow Transition and Turbulence



International Short Course Announcement

(Registration fee is $500 for students and $1000 for others)


Flow Transition and Turbulence - Physical Nature and High Order DNS Code



Registration for Remote Participant

FTT09 Agenda

User’s Agreement

FTT Course Content

Graphics by DNSUTA

Uniqueness of the Course

Dr. Kachanov’s CV

Local Organization

Local Arrangement

NSG People

Contact Info


CNSM Center









1. Date: May 11-15, 2009


2. Place:

103 PKH, 411 S. Nedderman, Department of Mathematics, University of Texas at Arlington, Texas 76019, USA


3. Principal Lecturer

Yury S. Kachanov, PhD, Professor

Institute of Theoretical and Applied Mechanics

Siberian Branch, Russian Academy of Sciences,

630090 Novosibirsk, Russia

Email: Kachanov@uta.edu



4. Content:


Part I Physical Nature -Turbulence Origin in Boundary-Layer Flows, Predominant Mechanisms and Applications (Yury S. Kachanov)


1)      Introduction

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 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)


5. Contact:

For more information, please contact

Chaoqun Liu, PhD

Professor and Director

Center for Numerical Simulation & Modeling

Department of Mathematics

456 PKH, 411 S. Nedderman, Box 19408

University of Texas at Arlington

Arlington, TX 76019-0408, USA

Email: cliu@uta.edu

Phone: 817-272-5151

Fax: 817-272-5802



6. Web Link:



Home | Faculty | GTAs | Undergraduate Program | Graduate Program | Research | Seminars

Teaching | Advisers | Computer Labs | Math Clinic | Math Placement Test | Contact Us

2001 The University of Texas at Arlington

Department of Mathematics, Box 19408, Arlington, Texas 76019-0408

Phone 817.272.3261 | Fax 817.272.5802 | math@uta.edu


Questions about this site? Email: Webmaster