Derivation of shock front evolution with rarefaction wave and its verification in dusty plasma simulations

Abstract

The evolution of unsupported shocks is theoretically investigated using the method of characteristics. It is found that the location and the speed of the generated non-uniform shock (NUS) front vary with the propagation time and the initial compression strength. The relationship between the NUS front location and the propagation time is asymptotically parabolic, while the speed of the NUS front decreases gradually with the propagation time. These analytical derivations are verified using computer simulations of unsupported shocks in 2D dusty plasmas performed here. The transition of the NUS front speed found previously [Sun et al., Phys. Plasmas 28, 103703 (2021)] using data fitting with the simulation data is re-investigated and further confirmed with the theoretical derivation of the NUS front in the current investigation.