# COMPUTATIONAL FLUID DYNAMICS

Academic Year 2019/2020 - 1° Year
Teaching Staff: Sebastiano BOSCARINO
Credit Value: 6
Scientific field: MAT/08 - Numerical analysis
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester:

## Learning Objectives

The objective of the course of Computational Fluid Dynamics is to introduce numericla methods for the numerical solution of systems that describe the compressible and incompressible flows.

## Course Structure

Hyperbolic systems.

Euler equation for the compressible gas dynamics.

Numerical methods for conservation laws.

Incompressible fluid dynamics.

Shallow water equations.

## Detailed Course Content

Waves: scalar equations, linear and non-linear case, characteristic methods. Viscosity solutions and entropy conditions. Hyperbolic systems: linear, semilinear e quasi-linear. Weak soluzions and jump conditions. Entropy conditions. Euler and Navier Stokes equatins. Simple wave in gasdynamics. Politropic Gas. Isentropic Gas dynamics. Rankine-Hugoniot conditions, shocks a discontinuity. Piston problem Riemann problem. boundary conditions. Finite volume methods: upwind method, Lax-Friedrichs method and Lax-Wendroff method. Godunov methods. Numerical Flux. High order methods. Essentially non oscillatory (ENO) and weighted Essentially non oscillatory (WENO). Conservative finite difference methods. Numerical integration: Runge-Kutta SSP (Strongly Stability Preserving) methods. Sourse term, Runge-Kutta IMEX (IMplici-EXplicit) methods. Incompressible Eulero and Navier-Stokes eqautions. Finite difgferenc e metthods for Euler and Navier-Stokes in primitive variables. Chorin projection method and MAC discretization (Marker and cell). Vorticity-stream function for Navier-Stokes equations. Saint-Venant model for shallow water euqations. Finite volume and finirte difference for SV equations in one and two dimensions. well-balanced methods.

## Textbook Information

--John D. Anderson Jr., Computational Fluid Dynamics, the basics with applications, McGraw Series in Mechanical Engineering, 1995.

-- Dimitris Drikakis, William Rider, High-Resolution Methods for Incompressible and Low-Speed Flows, Springer, 2005.

-- Joel H. Ferziger, Milovan Peric, Computarional Methods for Fluid Dynamics, Springer, 2002.

-- Randall Le Veque- Finite Volume Methods for hyperbolic problems, Cambridge University Press, 2004. Specializzato sui metodi ai volumi finiti per sistemi di iperbolici di leggi di conservazione.

--Randall Le Veque - Numerical methods for conservation laws, Lecture Notes in Mathematics, ETH Zürich, Birkhaeuser, Second edition, 1999.

--Roger Peyret, Thomas D. Taylor, Computational Methods for Fluid Flows, Springer-Verlag, 1983.

--Pieter Wesseling, Principles of Computational Fluid Dynamics, Springer Series in Computational Mathematics, 1991.

-- G.B.Whitham, Linear and nonlinear waves, John Wiley & Sons, 1974.