Many processes in natural and engineering sciences are mathematically described by systems of nonlinear partial differential equations. Any approach towards a deeper understanding and simulation of these processes requires a close interplay between mathematical modelling, analysis and numerics. The group aims at to make major contributions to these topics in an interdisciplinary context. A particular focus is on problems in mathematical fluid mechanics that lead to systems of conservation laws. Applications include multiscale and multiphysics problems in compressible fluid flow, multiphase flow in free and porous media domains, radiation- and magnetohydrodynamics as well as particle flow.