On Stability of Curvilinear Shock Wave in a Viscous Gas

The planar shock wave in a viscous gas which is treated as a strong discontinuity is unstable against small perturbations. As in the case of a planar shock wave we suggest such boundary conditions that the linear initial-boundary value problem on the stability of a curvilinear shock wave (subject to these boundary conditions) is well-posed. We also propose a new effective computational algorithm for investigation the stability. This algorithm uses the nonstationary regularization, the method of lines, the stabilization method, the spline function technique and the sweep method. Applying it we succeed to obtain the stationary solution of the considered boundary-value problem justifying the stability of shock wave.