High resolution hydrodynamic schemes and their implementation on vector computers

We present a short review of a class of so-called high resolution schemes for the numerical solution of the equations of compressible fluid flow and consider their implementation on vector computers. All schemes considered are Godunov-type of flux vector splitting schemes, based on approximate Riemann solutions and the splitting of the flux vector into fluxes to the right and left, respectively. They capture shocks sharply and monotonously without introducing spurious oscillations, while they are second order accurate in smooth parts of flow. Their efficient implementation on vector computers is discussed in detail. Computational results are given for the interaction of shock waves with complicated obstacles. A technique to introduce obstacles in the computational domain is presented. (orig./DG)