Turbulence Models and Numerical Solution of Turbulent Flow
Code  Completion  Credits  Range 

W01F001  ZK  60 
 Lecturer:
 Petr Louda
 Tutor:
 Petr Louda
 Supervisor:
 Department of Technical Mathematics
 Synopsis:

Basic characteristics of turbulent flow; governing equations; turbulent shear flow and thin shear flows; eddy viscosity turbulence models; Reynolds stress turbulence models; algebraic Reynolds stress models; low Reynolds number modifications; modelling transition to turbulence; numerical solution of averaged NavierStokes equations; examples of simulations.
 Requirements:
 Syllabus of lectures:

1. introduction to turbulent flow, mathematical and physical model, different approaches (DNS, LES, RANS)
2. mathematical properties of equations for RANS, LES, DNS. The role of convective and viscous term in turbulence; basic solution methods for incompressible flow.
3. basic governing equations; averaging; constitutive relations.
4. discretization methods from the point of view of turbulent simulations; numerical viscosity and dispersion; convectiondiffusion model equation.
5. closures for averaged NavierStokes equations; Boussinesq hypothesis; algebraic models.
6. Basics of LES; filtering; algebraic turbulence models; discretization and boundarz conditions; data processing; examples.
7. one and twoequation eddy viscosity models.
8. LES: continued.
9. low Re modifications; model with transport equation for eddy viscosity.
10. Solution of RANS equations; examples.
11. Reynolds stress turbulence models.
12. RANS simulations: channel flow and other examples.
13. algebraic Reynolds stress models; modelling laminar/turbulent transition
14. RANS simulations: continued
 Syllabus of tutorials:

1. introduction to turbulent flow, mathematical and physical model, different approaches (DNS, LES, RANS)
2. mathematical properties of equations for RANS, LES, DNS. The role of convective and viscous term in turbulence; basic solution methods for incompressible flow.
3. basic governing equations; averaging; constitutive relations.
4. discretization methods from the point of view of turbulent simulations; numerical viscosity and dispersion; convectiondiffusion model equation.
5. closures for averaged NavierStokes equations; Boussinesq hypothesis; algebraic models.
6. Basics of LES; filtering; algebraic turbulence models; discretization and boundarz conditions; data processing; examples.
7. one and twoequation eddy viscosity models.
8. LES: continued.
9. low Re modifications; model with transport equation for eddy viscosity.
10. Solution of RANS equations; examples.
11. Reynolds stress turbulence models.
12. RANS simulations: channel flow and other examples.
13. algebraic Reynolds stress models; modelling laminar/turbulent transition
14. RANS simulations: continued
 Study Objective:
 Study materials:

Wilcox D.C.: Turbulence Modeling for CFD, La Canada, DCW Industries, 1993
Ferziger J.H., Peric M.: Computational Methods for Fluid Dynamics, Springer Berlin, 1996
Piquet J.: Turbulent Flows  Models and Physics, Springer Berlin, 1999
Pope S.B.: Turbulent Flows, Cambridge University Press, 2000
Příhoda J., Louda P. Matematické modelování turbulentního proudění, Nakladatelství ČVUT, Praha 2007
 Note:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans: