# Computational fluid mechanics 1

## Presentation

Part 1: Fluid Mechanics

Fluid physical properties

General conservation laws for viscous compressible Newtonian fluids

Dimensionless numbers (Reynolds, Mach …)

Viscous flows

Perfect fluid flows. Bernoulli theorem and its applications

Elementary boundary layer theory for laminar flows

Capillary effects

Tutorials: sound propagation, surface wave propagation, Magnus effect, Drag and Lift forces, pressure loss, Jurin law …

Part 2: Finite volume method

Mathematical study of first order scalar conservation laws: method of characteristics, weak solutions, Riemann problem, Kruskov theorem

Principles of the finite volume method

Explicit versus implicit schemes

Godunov scheme, Roe scheme …

Discrete maximum principle, TVD schemes, CFL condition

Labwork: Finite volume method applied to the solution of the traffic flow equation.

## Objectives

At the end of this module, the student should have understood the fundamental notions and principles of fluid mechanics and finite volume method:

-       Mass, Momentum and Energy conservation laws for fluids,

-       Compressible / incompressible, viscous / inviscid, laminar/ turbulent flows,

-       Boundary layer flows,

-        Dimensionless equations (Reynolds number, Mach number, Froude number, Bond number …)

-       Godunov and Roe finite volume schemes, TVD schemes.

The student will be able to:

-       Solve some fluid mechanics problem by using analytical methods

-       Compute orders of magnitude and predict qualitative behaviour of simple flows,

-       Use finite volumes schemes to solve non-linear scalar conservation laws

## Needed prerequisite

Basis of general mechanics, continuum mechanics, numerical analysis and p.d.e. equations.

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...