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.
- 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.
There will be lectures by practitioners on topics of climate, combustion and other applications.