Mathematics

The course provides an introduction to the numerical simulation of laminar and turbulent incompressible flows by using a finite volume method. Each topic will be corroborated by a set of numerical examples to be performed within the open source C++ finite volume library OpenFOAM.

Module 0

• Well posedness of an abstract problem
• Numerical approximation of an abstract problem: consistency, convergence and stability
• Lax–Richtmyer theorem

Module 1

• Derivation of finite difference schemes
• Discretization of Ordinary Differential Equations: truncation error, Von Neumann stability analysis
• Discretization of Partial Differential Equations: truncation error, Von Neumann stability analysis

Module 2

• Introduction to Finite Volume discretization
• Derivation and discretization of Navier-Stokes equations in primitive variables
• Navier-Stokes equations in stream function-vorticity formulation

Module 3

• Some insights about the turbulence modelling: RANS and LES approaches
• LES modelling for Quasi Geostrophic equations

Please contact mgirfogl@sissa.it if you need more info.