Global Far-Field Computational Boundary Conditions for C- and 0-Grid Topologies

Abstract

Global far-field computational boundary conditions for inviscid external flow problems have been developed for C- and O-grid topologies. This analysis represents a unified approach for two-dimensional external flow problems. These boundary conditions are derived from analytic solutions of an asymptotic form of the steady-state Euler equations and have improved accuracy compared to characteristic boundary conditions commonly used in practice. The Euler equations are asymptotically linearized about a constant pressure, rectilinear flow condition, which is the true boundary condition at infinity. Previous work had developed higher-order boundary conditions for C-grid topologies by assuming small perturbations in both pressure and flow direction at and beyond the computational boundary, by decoupling the inflow and outflow analyses, and by linearizing the thermodynamic relations. This work lifts these restrictions, although some higher-order compressibility effects are neglected. It is based on a global mapping of the boundary and solution of the resulting Dirichlet-Neumann problem. Because the Euler equations are used to develop the boundary conditions, the flow crossing the boundary can be rotational. The boundary conditions can be used with any numerical Euler solution method and allow computational boundaries to be located very close to the nonlinear region of interest. This leads to a significant reduction in the number of grid points required for numerical solution. Numerical results are presented that show that the boundary conditions and far-field analytic solutions provide a smooth transition across a computational boundary to the true far-field conditions at infinity. They also demonstrate the synergism that can be realized from coupling analytic and computational methods.