On Stability of Curvilinear Shock Wave in a Viscous Gas

Abstract

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 curv ilinear shock wave (subject to these boundary conditions) is well-posed. We also propose a new effective computational algorith m for investigation the stability. This algorithm uses the nonstationary regularizat ion, the method of lines, the stabilizat ion 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.