ON ONE-DIMENSIONAL PLANAR AND NONPLANAR SHOCK-WAVES IN A RELAXING GAS

The paper examines the evolutionary behavior of shock waves of arbitra ry strength propagating through a relaxing gas in a duct with spatiall y varying cross section. An infinite system of transport equations, go verning the strength of a shock wave and the induced discontinuities b ehind it, are derived in order to study the kinematics of the shock fr ont. The infinite system of transport equations, when subjected to a t runcation approximation, provides an efficient system of only finite n umber of ordinary differential equations describing the shock propagat ion problem. The analysis, which accounts for the dynamical coupling b etween the shock fronts and the flow behind them, describes correctly the nonlinear steepening effects of the flow behind the shocks. Effect s of relaxation on the evolutionary behavior of shocks are discussed. The first-order truncation approximation accurately describes the deca y behavior of weak shocks; the usual decay laws for weak shocks in a n onrelaxing gas are exactly recovered. The results concerning shocks of arbitrary strength are compared with the characteristic rule. In the limit of vanishing shock strength, the transport equation for the firs t-order induced discontinuity leads to an exact description of an acce leration wave. In the strong shock limit, the second-order truncation criterion leads to a propagation law for imploding shocks which is in agreement (within 5% error) with the Guderley's exact similarity solut ion.