Finite-strength shock propagation for alternative equations of state

A systematic method of making calculations for finite-strength, i.e., nonself-similar, shock waves is developed. Using concepts of Lie groups, the invariance properties of the spherically symmetric equations of gasdynamics are determined and used to construct invariant equations of state. The invariant functions of this group are next introduced as the new dependent and independent variables along with an additional independent variable, the inverse square of the Mach number. The new dependent variables are then expanded in a power-series of the inverse square of the Mach number. The zero-order terms correspond to the self-similar results with the higher-order terms being perturbative corrections accounting for nonself-similar effects. Finally, example calculations are made for several different equations of state.U of I OnlyETDs are only available to UIUC Users without author permissio