Fluid-Structure Simulation of a Piston Shock-Tube Using an Adaptive ALE Scheme in the Non-ideal Compressible-Fluid Regime

Numerical simulations of the three-dimensional piston-induced shock-tube problem in Non-Ideal Compressible-Fluid Dynamics are performed by using a novel interpolation-free adaptive scheme, able to solve the Euler equations within the Arbitrary Lagrangian Eulerian (ALE) framework, including connectivity changes due to mesh adaptation. To cope with displacement- and force-imposed boundary motions, the grid is adapted by means of node insertion, deletion and edge swapping. The Geometric Conservation Law constraint is automatically fulfilled by an appropriate computation of the geometric grid quantities and no interpolation of the solution from the original to the adapted grid is required thanks to the interpretation of the connectivity changes as a sequence of fictitious continuous deformations. These capabilities represent great advantages with respect to standard interpolation-based adaptation techniques as they avoid the occurrence of spurious oscillations in the flow field, which may undermine the robustness of the numerical scheme in the non-ideal compressible-fluid dynamics regime in the close proximity of the liquid-vapor saturation curve and critical point. Numerical simulations confirm the feasibility of an oscillating-piston experiment to observe non-ideal wave propagation including non-monotone sound speed effects.