 # Modelling and Numerical Analysis in Fluid Mechanics

## Presentation

Programme (detailed contents):

From the Navier-Stokes model, we develop restricted models of incompressible flows such as Stokes (creeping flow), Euler (inertial flow without viscosity), Prandtl (boundary layer) and Reynolds (turbulent flow). We describe the following concepts of fluid mechanics: theorem of Euler, theorem of Bernoulli, inviscid flow, irrotational flow, fluid wall interaction (dynamics and thermal boundary layers), drag coefficient. Turbulence is described through the concept of turbulent viscosity, the universal logarithmic profile, the k-epsilon model and the different scales of turbulence.

We present the mathematical tools for solving least-square problems, non-linear equations and ordinary differential equations. We implement the methods in MATLAB software for its extensive use later on.

We also develop methods for numerical solutions of partial differential equations: stationary or time-variation problems with boundary conditions. We present the classification of differential problems of second order, and the different types of boundary conditions. The finite difference method is used for solving elliptic and parabolic problems. The problems of fully developed pipe flow in laminar and turbulent regimes illustrate this part of the course.

## Objectives

Acquire the basics of modelling in fluid mechanics to address the unit operations of process engineering and hydraulic engineering. Acquire the basic tools of numerical analysis and master the use of MATLAB. Acquire the tools for numerical simulation of partial differential equations and master their use in order to solve examples in real life, especially in fluid mechanics.

1. Understand energy balance and apply Bernoulli theorem
2. Master the concept of dynamic and thermal boundary layer to use transfer coefficients
3. Write a force balance on a inclusion with the correct drag coefficient expression
4. Write and use the universal velocity profile in turbulent flow
5. Estimate the space and time scales of turbulence in reactors
6. Know the basic tools of numerical analysis
7. Master the use of Matlab software
8. Know and use the numerical simulation tools to solve EDO and EDP.

## Needed prerequisite

UF Transport phenomena and reaction in fluids I2BETF11

UF Algebra and Analysis I2BEMT11

UF Analysis and computing I2BEIF11

## 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...