New explicit second order splitting-up schemes for the computation of steady and unsteady flows

Classes of splitting-up schemes for the solution of three-dimensional Euler equations and fully time-dependent compressible viscous Navier-Stokes equations yield results for the cases of inviscid transonic steady or unsteady two-dimensional flows with shocks, and of three-dimensional turbomachine flows, which indicate that these schemes are well adapted for such computations. Novel classes of optimal splitting-up schemes are also presented, including a dissipation-optimal scheme for the solution of a steady or unsteady shock problem that yields a numerically stable solution without artificial viscosity, and time-optimal splitting-up schemes for the solution of the Euler and Navier-Stokes equations.