Course # 4 : Computational Fluid Dynamics 1 : basic discretisation and time stepping methods

Course contents

1. Introductory lecture (G. Ghorbaniasl)
   • RANS-equations
   • finite volume methods
   • central discretisation with artificial viscosity of convective terms
2. Upwind space discretisations (G. Ghorbaniasl)
   • upwind discretisation of scalar convection
   • MUSCL
   • TVD-limiters
   • flux-difference splitting
   • symmetric TVD
3. Space discretisation of systems of equations (G. Ghorbaniasl)
   • extension to 1D and multidimensional Euler equations
   • central scheme with matrix dissipation
   •  discretisation of viscous terms
4. Explicit time stepping methods (G. Ghorbaniasl)
   • time discretisation
   • Runge-Kutta stepping and residual smoothing
    
5. Implicit time stepping methods (E. Dick)
   • stability regions of explicit and implicit time-stepping methods
   • need for implicit time stepping: slowly time-varying or steady flow, acoustic stiffness, geometric stiffness
   • system solvers: direct methods, iterative methods of factorisation, relaxation and minimum residual type, combination of factorisation and relaxation: LU-SGS, matrix-free formulation
   • convergence acceleration of iterative methods through multigrid and generalised minimum residual formulation
6. Semi-implicit time stepping methods (E. Dick)
   • acoustic properties of the flow equations
   • time-derivative preconditioning, artificial compressibility, dual time stepping
   • line-type semi-implicit stepping
   • segregated-type semi-implicit stepping: pressure-correction, momentum-interpolation
   • coupled pressure and temperature correction

Student assignment
The student will choose or receive an article and the examination will consist in a discussion on this subject.

Planning

• 6 lectures of 3 hours each, on Tuesdays and Wednesdays from 14.00 till 17.00 :
  1. Wed April 18, 2012
  2. Wed April 25, 2012
  3. Wed May 2, 2012
  4. Wed May 9, 2012
  5. Tue May 15, 2012
  6. Tue May 22, 2012
• place
  • lectures 1 through 4 will be given by G. Ghorbaniasl, at VUB, Triomflaan 43, Brussel (seminar room, take stairs in the back of the laboratory)
  • lectures 5 and 6 will be given by E. Dick, at UGent, Sint-Pietersnieuwstraat 41, Gent, Technicum, (item 2 on the map), blok A, room 308