Jz. Xu et al., ARTIFICIAL VISCOSITY IN THE TRANSONIC STREAM FUNCTION FORMULATION, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 38(7), 1995, pp. 827-837
The artificial density method which has been applied widely in the tra
nsonic potential calculation and the current transonic stream function
calculation is investigated theoretically. The analysis shows that in
the stream function formulation the artificial density is not equival
ent to the artificial viscosity and cannot be used, and a correct expr
ession of the artificial viscosity in the stream function method is th
en derived. The principal equation of the stream function, the density
equation converted from one of the momentum equations and the present
artificial viscosity scheme constitute the complete transonic stream
function formulation. The numerical practice demonstrates that the ran
ge of Mach number computed by this approach is extended and the shock
location is close to the experimental result.