Computational Fluid Dynamics

Institution: DICAR (UNIPV)

Major: HYRIS

Term: 2nd Semester – Academic Year 2018-2019

Instructors: Stefano Sibilla (, Andrea Fenocchi (

CFU: 6


Duration: 03/04/2019 – 16/05/2019


– Tuesday 11:00 – 13:00 (E7, Engineering Campus)

– Wednesady 11:00 – 13:00  and 14:00 – 16:00  (E7)

– Thursday 11:00 – 13:00  and 14:00 – 16:00  (E7)

– Friday 11:00 – 13:00  (F2: April 5th and 12th; E7: May 3rd and 10th)


Office hours: Wednesday 2-4 PM



The course will give students a basic knowledge of the numerical methods applied to solve problems in the fields of hydraulics and fluid dynamics, learning to apply them with awareness also through the use of dedicated software.



  1. Equations of fluid mechanics: conservation of mass and momentum; Navier-Stokes equations; Shallow Water equations.
  2. Discretization methods: i) Finite Differences method: accuracy, stability and numerical diffusion;ii) Finite Volumes method:upwind methods and the Riemann problem.
  3. Numerical solution of the Navier-Stokes equations: linearisation methods for the convective terms;projection methods for incompressible fluids; treatment of the free surface in Eulerian schemes: the Volume of Fluidmethod.
  4. Introduction to the numerical solution of the Shallow Water equations.
  5. Turbulence modeling: turbulent flow theory; Reynolds-Averaged Navier-Stokes equations;turbulent kinetic energy and its dissipation; k-ε method.
  6. Smoothed Particle Hydrodynamics: kernel approximation and particle approximation; SPH solution of the Navier-Stokes and Shallow Water equations;enforcement of boundary conditions.



Basic knowledge of Hydraulics, Fluid Mechanics and Numerical Analysis



J.H. Ferziger, M. Peric. (2002) Computational methods for fluid dynamics. Springer. 423 pp.



Assignments will be handedover and evaluated during the course.The final examination will consist of a 2/3 hour-long written test. The finalexam format is closed-book only. An equationsheet will be provided if needed.Students will be admittedto the final exam based on a satisfactory performance in the assignments.