CE 580 COMPUTATIONAL TECHNIQUES FOR FLUID DYNAMICS

Instructor: Dr. İsmail Aydın                                                                                    Spring, 2018

Contents

  1. INTRODUCTION (4 hrs.)
    • Theoretical, experimental and computational approaches
    • Components of a numerical solution and a CFD code
    • Governing equations of fluid flow
    • Reynolds averaged Navier Stokes (RANS) equations
    • Introduction to turbulence modeling
  1. FINITE DIFFERENCE METHODS (FDM) (12 hrs.)
    • Finite difference representation of derivatives
    • Variable mesh systems
    • Difference representation of PDEs and related concepts
    • Stability considerations
    • Modified equation
    • Application of FDM to selected model equations
      • Heat equation
      • Wave equation
      • Burgers equation
      • Laplace equation
  1. FDM FOR THE NAVIER STOKES EQUATIONS (8 hrs)
    • Vorticity-stream function approach
    • ADI solution
    • Poisson equation for pressure
    • Primitive variables approach
    • SIMPLE
    • Artificial compressibility method
  1. FINITE VOLUME METHOD (FVM) (15 hrs.)
    • Generic conservation equation
    • Approximation of integral equation on structured grid
    • FVM on complex geometries, use of unstructured grid
    • FVM for non-linear shallow water equations
  1. GRID GENERATION (3 hrs.)
    • Structured and unstructured grids
    • Grid generation techniques
    • Generalized transformation of the governing equations
    • Algebraic grid generation

 

Homework assignments:

  1. Transient pipe flow.
  2. Laminar flow between parallel plates. (errors)
  3. Implicit solution to turbulent flow between parallel plates.
  4. Explicit solution to turbulent pipe flow.
  5. Water surface profile for wave motion in a rectangular basin.
  6. Best overrelaxation parameter in SOR methods.
  7. ADI solution to vorticity-stream function formulation of cavity flow.
  8. Turbulent pipe flow solution using wall functions
  9. Flow over Backward Facing Step using u-v-p formulation.
  10. 2D shallow flow solution around a rectangular bridge pier.

 

References:

  • An Introduction to Computational Fluid Dynamics, The Finite Volume Method’, H. K. Versteeg, W. Malalasekera, Longman, 2007
  • Computational Methods for Fluid Dynamics’, J. H. Ferziger, M. Peric, Springer-Verlag, 2002
  • Numerical Simulation in Fluid Dynamics’, M. Griebel, T. Dornseifer, T. Neunhoeffer, SIAM, 1998
  • Numerical Computation of Internal and External Flows’, C. Hirsch, John Wiley & Sons, 1997
  • Computational Fluid Dynamics’, J. D. Anderson, McGraw-Hill, 1995
  • Computational Fluid Dynamics for Engineers’, K. A. Hoffman, S. T. Chiang, Engineering Education System, P.O. Box. 20078 Wichita, KS 67208-1078, USA, 1993
  • Computational Fluid Dynamics, An introduction for Engineers’ M. B. Abbott, D. R. Basco, Longman, 1990
  • Computational Fluid Mechanics and Heat Transfer’, D.A. Anderson, J.C. Tannehill, R.H. Pletcher, McGraw-Hill, 1984
  • Computational Methods for Fluid Flow’, R. Peyret, T.D. Taylor, Springer–Verlag, NewYork, 1983

 

Grading:                  Homework                : 40%

Midterm Exam         : 20%

Final Exam              : 40%

Schedule: Wednesday, 8:40-11:30,  Room K3-102

FIRST MEETING WILL BE

on February 14th, Wednesday, at 9:00, in K3-102