Numerical solution of inviscid and viscous flows using modern schemes and quadrilateral or triangular mesh

summary:This contribution deals with the modern finite volume schemes solving the Euler and Navier-Stokes equations for transonic flow problems. We will mention the TVD theory for first order schemes and some numerical examples obtained by 2D central and upwind schemes for 2D transonic flows in the GAMM channel or through the SE 1050 turbine of Škoda Plzeň. The TVD MacCormack method is extended to a 3D method for solving flows through turbine cascades. Numerical examples of unsteady transonic viscous (laminar) flows through the DCA 8% cascade are also presented for $\text{Re}=4600$. Next, a new finite volume implicit scheme is presented for the case of unstructured meshes (with both triangular and quadrilateral cells) and inviscid compressible flows through the GAMM channel as well as the SE 1050 turbine cascade