This project concerns the development of new structure preserving numerical schemes for nonlinear time-dependent hyperbolic PDE systems with particular focus on new numerical methods on general unstructured meshes asymptotically consistent with the fluid and solid limits of the Godunov-Peshkov-Romenski model for continuum mechanics, novel algorithms for hyperbolic PDE with involution constraints of the curl type and new schemes for overdetermined hyperbolic PDE systems that are exactly and provably thermodynamically compatible.

Potential applications lie in the fields of computational fluid and solid mechanics, particular geophysical flows relevant for environmental and coastal engineering and civil protection, compressible single and multi-phase flows in mechanical, industrial and aerospace engineering, and in the simulation of blood flow and fluid-structure interaction (FSI) problems in medicine.