Self-similar solutions in gas dynamics with exponential time dependence

Self-similar gas flow with similarity coordinate xi=re(-/+t), exponential in time, is investigated for plane, cylindrical and spherical geometry. The underlying Lie group symmetry is pointed out and also how it is obtained from flow with power-law self-similarity (xi=r/\t\(alpha)) in the limit alpha-->infinity. Six distinct types of solutions are derived and plotted in r-t coordinates. They are characterized by steep density gradients. Also, solutions with strong shock boundaries are discussed. A completely analytical solution is presented, related to Sedov's solution of a strong point explosion. (C) 1997 American Institute of Physics.