Scope: The course is about a broad class of advanced
numerical methods for solving partial differential equations
that model a variety of physical/chemical processes of
interest to industry, academia and research organizations.
The emphasis is on basic concepts and the foundations
required for algorithm design, code development and
practical applications.

Who should attend: The course is suitable to doctoral
students, post-doctoral research fellows, academics involved
in the teaching of numerical methods, researchers from
industry, research  institutions and consultancy
organizations. The course may also help those in managerial
and policy-making positions.

Working plan: The theory given in two daily morning sessions
will be supplemented with laboratory-based exercises and
case studies, as well as with carefully selected lectures
given by prominent scientists involved in solving real problems.

Contents:

    * Mathematical models for the simulation of processes in
physics, chemistry and others.
    * Hyperbolic conservation laws. The Riemann problem.
    * Basics on numerical approximation of partial
differential equations:
      finite differences, truncation error, accuracy,
stability, conservative methods.
    * The finite volume and DG finite element approaches.
    * Riemann solvers for gas dynamics, shallow water and
compressible multiphase flows.
    * High-order methods: spurious oscillations, Godunov’s
theorem and non-linear schemes.
    * TVD methods.
    * Source terms, diffusion terms and multiple space
dimensions.
    * ADER methods in the finite volume and DG frameworks,
with ENO and WENO reconstruction.