MODELING OF HYPERSONIC FLOWS: INFLUENCE OF THE STARTING CONDITIONS OF THE ALGORITHM ON THE FINAL SOLUTION IN THE VICINITY OF BIFURCATION POINTSG. A. Tarnavskii,a G. S. Khakimzyanov,b and A. G. Tarnavskiic UDC 519.6:531.332 We investigate the influence of the starting conditions of the computational algorithm (a discrete analog of the initial data of a continuous differential problem) on the trajectory of calculation advancement in the space of solutions and on the obtained final (stationary, quasi-stationary, or nonstationary) solutions of Navier-Stokes equations for mathematical modeling of high-speed gas flows. Particular consideration is given to the analysis of the behavior of trajectories in the vicinity of the bifurcation points of branching of solutions. Questions associated with the "carbuncle" effect - a special kind of instability of a part of the shock front at a hypersonic flow over the front part of a blunt-nosed body - are discussed. aInstitute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, 4/1 Institutskaya Str., Novosibirsk, 630090, Russia; email: email@example.com; bInstitute of Computer Technologies, Siberian Branch of the Russian Academy of Sciences; email: firstname.lastname@example.org; cNovosibirsk State University; email: email@example.com. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 5, pp. 54-60, September-October, 2003. Original article submitted November 4, 2002.