modern schemes for computation of transonic flows in internal aerodynamics

The work deals with numerical solution of steady transonic flows with applications in internal aerodynamics. The problems are described by the system of 2D or 3D Euler or Navier-Stokes equations. Our group developed during last years several central or upwind TVD finite volume methods for computation of transonic flows through a cascade or in a channel using grids of quadrilateral cells or triangular cells. We also developed other (non TVD) schemes e.g. MacCormack scheme or several multistage Runge-Kutta finite volume schemes with applications of some acceleration techniques (multi-grid solution or hierarchical residual averaging). Our aim is to present some comparison of results of flows in internal aerodynamics using TVD schemes or other schemes. One can also compare the influence or artificial viscosity effects especially using TVD schemes.