What is the correct boundary to apply at the outlet when the inlet velocity varies rapidly from subsonic to supersonic conditions? 'Outlet'condition produces negative densities when flow is subsonic. Thanks.

(1). The correct boundary at the out let is the one which simulate your real "testing" condition. (2). In other words, your computational domain must be consistent with the real testing configuration. (3). When the flow is "subsonic", the region of influence is infinite, that is, it can reach almost everywhere. In that case, the selection of the outlet location is critical. Move it further away from the point of interest. (4). If the code is producing negative densities, then it is not a realistic code at all.