In the end, student must know the Finite Volume discretization technique which is often used in numerical tools (CFD codes in particular) in order to solve partial differential equations governing physical conservation laws. They must also be familiar with methodology elements for setting up numerical simulation in Computational Fluid Dynamics codes to solve physical problems.

Learning objectives

- Understand the spatial and temporal discretization schemes used in the finite volume technique
- Implement and use the finite volume technique on simple physical problems (conduction, convection)
- Understand the following concepts : convergence, initial conditions, relaxation
- Understand the following concepts : mesh, computational domain, boundary conditions
- Understand the importance to identify the physical models involved

Learning context

This course complements all courses dealing with fluid mechanics, heat transfer... It provides the concepts necessary for the resolution of the conservation equations by means of numerical tools.
It is complemented by a practical work "Flow in a Venturi tube : Theoretical Study, Experimental & Numerical Simulation" and also a "Project on applied Computational Fluid Dynamics”.

Course materials

Two handouts are provided :
Part A : The finite volume method
Part B : Methodology in numerical simulation
Copy of oral presentations materials are also provided.

Prerequisites

Science Fundamentals in fluid mechanics, heat transfer, numerical analysis

Course content

I- The finite volume method
A- Mathematical description of phenomena
B- The discretization methods
C- Resolution of the conduction equation
D- Convection and diffusion
E- Flow calculation
II- Methodology in numerical simulation
A- Introduction to Computational Fluid Dynamics
B- Creation of a model
C- Turbulence modeling
D- Boundary conditions