"In this project we develop new algorithms for the solution of general nonlinear systems of time dependent partial differential equations (PDE) in the context of non-ideal magnetized multi-fluid plasma flows with thermal radiation. We will produce new high order schemes on unstructured tetrahedral meshes that are applicable to a rather general class of problems in general geometries, thus opening a wide range of possible applications in science and engineering. We will consider both, Eulerian methods on fixed grids and Lagrangian schemes on moving meshes to reduce numerical diffusion at material interfaces. A particular feature of our schemes is that they are high-order one-step methods based on local space-time predictors that allow using time-accurate local time stepping, i.e. each element runs at its own optimal time step. Even nowadays better than second order accurate 3D unstructured Eulerian methods are very rare, but there is still no better than second order accurate unstructured Lagrangian scheme available on general tetrahedral meshes. To develop these missing algorithms is the objective of our research project.A very challenging application that we have in mind is inertial confinement fusion (ICF) which is highly relevant for modern society and its increasing need for clean and inexhaustible energy. It is believed that early ICF experiments in the 1970ies failed because they did not reach the necessary critical pressure and temperature due to hydrodynamic instabilities in the flow. In this project we propose to design algorithms for simulating ICF flows with billions of high order elements on up to 100,000 CPUs of modern supercomputers. We will also propose active control strategies based on adjoint equations to reduce the hydrodynamical instabilities. Hence this project aims at providing next-generation numerical modeling tools for a possible future scenario of clean civil energy production via ICF."