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
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.
* Mathematical models for the simulation of processes in
physics, chemistry and others.
* Hyperbolic conservation laws. The Riemann problem.
* Basics on numerical approximation of partial
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, Godunovâ€™s
theorem and non-linear schemes.
* TVD methods.
* Source terms, diffusion terms and multiple space
* ADER methods in the finite volume and DG frameworks,
with ENO and WENO reconstruction.