Wave drag determination in the transonic full-potential flow code matrics

Abstract

The mathematical background is described of a method that is currently being developed at NLR to calculated wave drag in transonic potential flow. The method is a generalization and extension of Garabedian's and McFadden's idea of determining wave drag by volume-integration of the artificial viscosity. The generalization of Garabedian's and McFadden's idea involves the introduction of a reference artificial viscosity which provides a solid theoretical basis. At the same time this ensures that calculated wave drag is to a certain extent independent of the specific details of the artificial viscosity in different codes. The extension of Garabedian's and McFaddens's idea accounts for the fact that artificial viscosity does not smear out supersonic/subsonic shock waves completely, but leaves room for a truly discontinuous sonic/subsonic "shock remainder" that contributes substantially to the wave drag. Both fully conservative and non-conservative shock capture in potential flow are covered. The method can be extended to handle also pseudo Rankine-Hugoniot shock waves. An illustrative example for a transonic transport type wing is given.