The duration of the summer school is estimated to be three days, its tentative structure is as follows:
Day 1. First an introduction to the analysis of conservation laws is given. In particular, the theory of scalar, non-linear hyperbolic conservation laws is discussed. As a building stone for both the analysis and the numerics, the so-called Riemann problem is discussed in detail.
Day 2. The content of day two is twofold. In the morning, the role of conservation laws in computational fluid dynamics is presented. First the equations describing fluid flow are derived, based on fundamental physical principles. In the afternoon, an introduction to numerical methods for the treatment of conservation laws is given. Based on the Riemann-problem, the participants will implement a conservation law solver in Matlab.
Day 3. Day three builds upon the content of days one and two and introduces the “Discontinuous Galerkin method”, a modern state-of-the-art solution technique for nonlinear systems of conservation laws. The open-source tool Netgen/NGSolve with its easy-to-handle Python interface is introduced to the participants and used in the exercises, so that discussed theoretical effects can be observed on the spot.
Day three ends with a dinner, giving the participants the possiblity to discuss matters and to build a network.