Adaptive Simulations of Cylindrical Shock Waves in Polytropic van der Waal Gas

Abstract

The propagation of converging cylindrical shock waves, collapsing at the axis of symmetry, in a non-ideal gas is investigated by using innovative interpolation-free mesh adaptation techniques. The high pressure, temperature, and energy that can be reached close to the focus point call for thermodynamic models able to take into account the non-ideal gas effects. A distinguishing feature of converging shock waves is the non-constant propagation speed, which makes the flow field behind the shock intrinsically unsteady. To efficiently simulate this configuration, it is fundamental to adapt the computational domain as time evolves. Hence, at each time step, we modify the grid spacing through node insertion, deletion, or relocation according to the current position of the flow features. In this work, any interpolation of the solution between the original and the adapted grids is avoided thanks to a peculiar strategy able to describe mesh adaptation within the arbitrary Lagrangian-Eulerian framework. The adaptive simulation framework, equipped with the polytropic van der Waals equation of state, is assessed first in dilute conditions, where it is possible to compare numerical results with theoretical predictions. In particular, we compute the Guderley-like self-similar solution describing shocks of different intensities propagating in the siloxane MM. Then, it is used to verify the possibility to reach higher energy density when the shock is initiated in the NICFD regime. Finally, we investigate the interaction between the converging shock wave and an arc-shaped obstacle, which is a fundamental phase of the so-called reshaping process, useful to increase the stability of converging shocks.