Very often in Astrophysics we have high-velocity fluid collisions, which we treat as Riemann problems (combinations of shock waves, rarefaction waves and contact discontinuities). We have studied and continue to work on their implementation on (i) Cepheid wind structure and its relation to recently observed phase-dependent X-ray emission, (ii) interaction of an AGN jet with its environment, (iii) role of rarefaction acceleration when a GRB jet crosses the surface of the progenitor star.