THE NUMERICAL SIMULATION OF JET EXIT PROBLEMS BY
           FINITE VOLUME  METHOD OF 2-ND ORDER OF ACCURACY.
                     S.N.Martyushov.
      The Institute of Mathematics and Mechanics, Ural Branch of
             Russian Academy of Sciences, Ekaterinburg, Russia.

   The unsteady flows,  arising from exit of jet to chambers of low
pressure are numerically simulated.  For account of real properties of
gas,  appearing at numerous passing of shock waves on calculation area
the barotropic equation of state, in particular, equation of state
with effective ratio of specific heat capacities is used.
     The method of finite volume,  based on calculation of flows  with
using of approximate Riemann invariants [1] is applied.  The order of
approximation in time and space is increased to second by applying
Harten method [2] in the algorithm. For construction of calculation
grids the algorithm, based on vector Poisson equation decision by SOR
iteration method [3] was applied. For geometrical adaptation of grid
to a priori known features of decision the control functions, i.e.,
the right parts of the vector Poisson equation, are used. The choosing
of these functions permits either to produce attraction-repulsion of
the grids in necessary locations or  to achieve orthogonality of it
on necessary parts of boundary.
     The lounching of Hartmann resonator from beginnings of jet exit to
exit of reflected shock wave from resonator for various  significances
of pressure  ratious  and  distance  of  aperture  from  resonator was
calculated. The exit of jet from chamber, modelling reflecting nozzle
was
also investigated. The formation of return flow, reflected  shock wave
and there displacement downwards of flow were observed.
   The exit of jet through nozzle with attachment, creating pulsations
was numerically simulated. The structure of arising vortex flow,
reflected  by  shock  wave,  locking  up  the  flow inside nozzle is
determinated.

 1. Gloester P. J. of Comp. Phys., Vol.77, p.361 (1988).
 2. Yee H.C., Warming R.F., Harten A. J. of Comp. Phys., Vol.57, p.327
(1985).
 3. Thompson J.F., Warsi Z.U.A., Mastin C.W. Numerical Grid Generation.
    Foundation and Application. North Holland, 1985, p.483.