The aerodynamic design of hypersonic vehicles envisaged for future defence applications, and UK-partnered planetary exploration plans (e.g. ExoMars in ESA's Aurora programme), is a major challenge due to the strong viscous effects (very high local heating rates and shock/shock interactions), the rarefaction phenomena characteristic of mixed-density flowfields, and the real-gas effects of high temperature (vibrational excitation, dissociation and ionization). Conventional fluid dynamics is often unsuitable for many aerothermodynamic situations, while statistical molecular dynamics is computationally too intensive. To address these twin problems we propose deploying extended hydrodynamics alongside a new continuum-fluid description of the non-equilibrium thermochemistry that incorporates both rarefaction and surface-catalycity. Extended hydrodynamics comprises high-order additions to the Navier-Stokes model that correct for rarefaction. It combines the computational efficiency of continuum-flow models with the major advantage that it reduces to the conventional Navier-Stokes model in near-equilibrium conditions.This is a new collaboration between Daresbury Laboratory and Strathclyde and Warwick Universities with the goal of building a new UK capability in high-speed mixed-density aerodynamic modelling. It is a Joint Grant Scheme proposal with the MoD's Defence Science and Technology Laboratory (Dstl), with additional support from MBDA and FGE. Dstl will provide experimental and computational data to help validate our models. They will also co-host with the applicants a one-day open workshop on high-speed flow modelling, which will act as a forum to discuss the future growth and direction of the UK high-speed flow research community.