Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids

Two-dimensional simulations are carried out to assess standard grid adaptation criteria, widely used for ideal flows, for steady inviscid flows in the proximity of the liquid-vapor saturation curve, where non-ideal compressible-fluid behavior is expected. A van der Waals fluid description of the thermodynamic properties is assumed to account for non-ideal effects at least qualitatively. Nitrogen under-expanded nozzle jets are chosen as the reference flow to assess different adaptation criteria. Isotropic and anisotropic error estimators based on the derivatives of flow variables prove to be suitable to capture the rarefaction, the reflected shock and the constant-pressure jet boundary. Both density and Mach-based estimators are found to be very suitable to drive grid adaptation in the non-ideal compressible-fluid regime, which is characterized by large fluid compressibility. Then, similar adaptation criteria are used to simulate under-expanded nozzle jets of the siloxane MDM, a high molecular complexity fluid for which the van der Waals model predicts the existence of a thermodynamic region where the fundamental derivative of gasdynamics has values less than one. In this region, Mach number estimators prove to be more effective because of the non-ideal dependence of the speed of sound on the density and the temperature.