Artificial viscosity in the transonic stream function formulation

摘要

The artificial density method which has been applied widely in the transonic 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 equivalent to the artificial viscosity and cannot be used, and a correct expression of the artificial viscosity in the stream function method is then 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 range of Mach number computed by this approach is extended and the shock location is close to the experimental result.