 # 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...