Symbolic-Numeric Stability Investigation of
            Difference Schemes for the Euler and Navier-Stokes
                              Equations

                  V.G. Ganzha*) and E.V. Vorozhtsov

             Institute of Theoretical and Applied Mechanics,
          Russian Academy of Sciences, Novosibirsk 630090, Russia
          -----------------------
          *) At the moment, the University of Kassel, Kassel D 34127, Germany

                                Abstract

            We present a number of the symbolic-numeric algorithms for the
       stability investigation of difference schemes approximating the 2D
       and 3D Euler and Navier-Stokes equations of the compressible fluids.
       All the algorithms implement in different ways the von Neumann
       stability analysis procedure. It is shown that the consideration of
       the curvilinear grid within the framework of the Fourier stability
       analysis method increases by a factor of 23/9 the number of
       nondimensional variables in the domain of the variation of which the
       stability region is then determined in comparison with the case of an
       uniform rectangular spatial grid for the difference discretization of
       the 3D thin-layer Navier-Stokes equations. Since the needed computer
       memory in the 3D case may reach O(10^107) machine words, the questions
       of the compression of intermediate algebraic expressions are
       discussed. A four-step stability analysis procedure for difference
       schemes on curvilinear grids is proposed. The influence of turbulence
       modeling on the sizes of the necessary stability region has been
       investigated. Computational examples are presented.