The effect of the artificial far field boundary on a finite different approximation of the Navier-Stokes equations for a compressible fluid

During this period the principal investigator has considered the effect of the artificial far field boundary on a finite different approximation of the Navier-Stokes equations for a compressible fluid considered for two dimensional boundary conditions for the far-field boundary can results in some of the following phenomena: (1) reflecting boundary conditions, in which the disturbances in the physical variables represented by the difference between the steady state flow and the initial conditions are not allowed to exit through the far-field boundary but instead continue echoing up and down the grid; (2) under-specified boundary conditions, in which the converged steady state solution may depend on the initial conditions; and (3) over-specified boundary conditions in which large errors are introduced before convergence takes place. The following conclusions may be drawn from the numerical experiments conducted as a part of the research effort: There are four distinct artificial nonreflecting boundaries containing free-stream information, these being the inflow, outflow, top-sidewall and bottom-sidewall. Each of these boundaries must be treated differentially, or errors are introduced into the system.