Upwind relaxation algorithm for re-entry nonequilibrium flows We describe the development of Navier-Stokes solver URANUS (Upwind Relaxation Algorithm for Nonequilibrium Flows of the University of Stuttgart), where advanced gas-phase and gas-surface interaction modeling allows an accurate prediction of thermochemical relaxation in high-temperature nonequilibrium flows around re-entry vehicles and the associated aerothermal surface loads. A fully coupled, fully implicit numerical algorithm, which solves the Newton-linearized equation system iteratively with arbitrary accuracy allows for large CFL numbers. Therefore, Newton-like convergence rates and a sufficient convergence grade are obtained for accurate computation of sensitive flow quantities like skin friction coefficient and Stanton number. The favorable performance of the algorithm is demonstrated for solutions of two- and three-dimensional sequential nonequilibrium codes on NEC SX-4.