The activities of the SINUS team aim at contributing to the progress of methods of numerical modelling, from the analysis of mathematical and physical models, to the computer implementation of the solution algorithms. Our efforts are to find new methods (approximation, solution algorithms), to analyse models and schemes, and to experiment them. Today's application domain is the simulation of compressible reactive flows (aerodynamics, hypersonics, combustion), with an extension to first--order hyperbolic systems in general. The main methods that are produced are : upwind TVD finite--element methods applicable to non--structured meshes, self--adaptive meshes, implicit and multigrid schemes, spectral methods, parallel algorithms ; these methods are to prepare a new generation of CFD codes that will be more friendly (due to more general meshes, to extra robustness provided by TVD and strongly implicit formulations), and more adapted to intensive/parallel calculations. Besides our colleagues of numerical methods, our usual collaborators are : physicists (for the analysis of fundamental phenomena, and help in modelling), computer scientists (software chain for parallelism with emphasis on numerics and environments), software industries (numerical methods, design of codes), application--oriented industries (contribution to physical modelling, numerical methods, design of codes).