EQUAL-ORDER INTERPOLATIONS - A UNIFIED APPROACH TO STABILIZE THE INCOMPRESSIBLE AND ADVECTIVE EFFECTS

In this paper we present a new SUPG formulation for compressible and n ear incompressible Navier-Stokes equations [5]. It introduces an exten sion of the exact solution for one-dimensional systems to the multidim ensional case, in a similar way to that arising in the scalar problem. It is important to note that this formulation satisfies both the one- dimensional advective-diffusive system limit case and the advection-do minated multidimensional system case presented by Mallet et al. Anothe r interesting feature of this formulation is that it introduces natura lly a stabilizing term for the incompressibility condition, in a simil ar way to that found by other authors [1-4]. However, in our formulati on the stabilization is introduced to the whole system of equations, w hile other authors introduce a term to stabilize the incompressibility condition and another one for the advective term. In Section 1 we pre sent Navier-Stokes equations for compressible flow and, then, we pass to detail several topics related to the numerical discretization of su ch advective-diffusive multidimensional systems of PDEs, in the Petrov -Galerkin context. The method is applicable and described for the gene ral Re > 0 laminar flow, but the nature of the stabilizing effect of t he artificial diffusion matrix introduced is discussed in depth for th e simpler Stokes (Re = 0) flow. Several numerical results are shown in Section 5, taking the well-known test problem of the square-cavity an d a variant of this, namely a multiply connected square-cavity, as a v alidation for this code.