This cours deals with a basic introduction to the numerical simulation of fluid flow, i.e., how to obtain a numerical solution to a fluid flow problem, how to discretize the underlying equations and how to evaluate the result.

Content:

• Governing equations and models in fluid mechanics

• Steady problems: the Finite-Difference Method (FDM)

• Unsteady problems: methods of time integration

• Advection-diffusion problems

• The Finite-Volume Method

• Solution of the incompressible Navier-Stokes equations

• Grids and their properties

• Boundary conditions

The students who successfully take this module should:

• understand the physical meaning and mathematical character of the terms in advection-diffusion equations and the Navier-Stokes equations

• assess under what circumstances some terms in these equations can be negelcted

• formulate a FDM for the solution of unsteady transport equations

• asess the convergence, consistency and stability of a FDM

• formulate a FVM for the solution of unsteady transport equations

• know how to solve the Navier-Stokes equation with the FVM

• implmement programs in matlab/octave to simulate fluid flow

• assess the quality and validity of a fluid flow simulation

• work in team and write a report describing the results and significance of a simulation

• know the different types of grids and when to use them