Supersonic inviscid flows in missile propulsive jet are simulated numerically with discontinuous finite element method based on twodimensional conservation laws, which is developed to solve axlsymmetric Euler equations. Computational results show good agreement with experimental data. The method shows higher resolution at discontinuous points compared with TVD schemes. It exhibits high capability in capturing shocks without numerical oscillation and artificial viscosity near discontinuous points.

According to the MUSCL scheme with some modifications, the flow field structure of jet is numerically simulated. The results show that the present scheme has high resolution of shock wave, nonoscillation and high efficiency.

A rapid convergence method for calculating all induced velocity components by contracted vortex lines(e.g., tip vortex and inboard vortex) is presented. The advantage of the method is, the induced velocities at any point in the wake can be calculated and the wake contraction is considered. Not only does it avoid the truncation errors associated with discretization of the vortex lines, but also reduces integrand errors corresponding to finite azimuthal angle. Therefore, both numerical precision and integrand convergence rate are obviously improved. This method is developed from Rand and Chiu's method(a rapid convergence method for computing the induced velocity by a helical vortex line), which is based on finding upper and lower bounds on the truncated integral.

When a shock wave propagates into a quiescent atmosphere of low pressure from a nozzle orifice, the flow can be simplied by solving a axisymmetric unsteady flow problem. In this paper second order accurate upwind schemes in total variation diminishing (TVD) type is employed for numerically simulating underexpanded supersonic free jet. A satisfactory time-dependent solution has been achieved.

In this article, we suggest a new linear function and prove that the MUSCL scheme would have second-order accuracy, if the function was used to approximate the initial-value distribution of flow variables in every mesh. The scheme is suitable for the Enlerian calculation when monotonicity condition and some dissipative mechanisms are introduced. We approximate the characteristic equations with shock jump relations near discontinuities and resolve the problem of using characteristic method in whole flowfield calculation. Finally, we present the numerical examples of Emery problem and a rocket jet problem.