COMPUTATIONAL FLUID DYNAMICS

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.

Hyperbolic systems.

Euler equation for the compressible gas dynamics.

Numerical methods for conservation laws.

Incompressible fluid dynamics.

Shallow water equations.

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.

--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.