NUMERICAL-SOLUTIONS OF EULER EQUATIONS BY USING A NEW FLUX VECTOR SPLITTING SCHEME

A new flux vector splitting scheme has been suggested in this paper. T his scheme uses the velocity component normal to the volume interface as the characteristic speed and yields the vanishing individual mass f lux at the stagnation. The numerical dissipation for the mass and mome ntum equations also vanishes with the Mach number approaching zero. On e of the diffusive terms of the energy equation does not vanish. But t he low numerical diffusion for viscous flows may be ensured by using h igher-order differencing. The scheme is very simple and easy to be imp lemented. The scheme has been applied to solve the one dimensional (1D ) and multidimensional Euler equations. The solutions are monotone and the normal shock wave profiles are crisp. For a ID shock tube problem with the shock and the contact discontinuities, the present scheme an d Roe scheme give very similar results, which are the best compared wi th those from Van Leer scheme and Liou-Steffen's advection upstream sp litting method (AUSM) scheme. For the multidimensional transonic flows , the sharp monotone normal shock wave profiles with mostly one transi tion zone are obtained. The results are compared with those from Van L eer scheme, AUSM and also with the experiment.