Finite element modeling of non-equilibrium fluid-wall interaction beyond the continuum regime

The numerical modeling of the aerodynamic interactions at high-altitudes and high-Mach numbers is considered in view of its importance when studying problems where the continuum hypothesis at the foundation of the Navier-Stokes equations becomes invalid. One of the difficulties associated with these flight conditions is that both the velocity and the temperature of the fluid do not abide by the no - slip conditions at the wall. A weak-Galerkin Finite Element formulation of the Maxwell-Smoluchowsky model is introduced to discretize the velocity slip and temperature jump conditions with better accuracy than the standard Finite Element approximation. The methodology is assessed on configurations such as cylinders and spheres for flow conditions ranging from quasi-equilibrium to non-equilibrium. Improvements are observed in the slip regime compared to available data. Nonetheless, the results in the transition regime highlight the need for more sophisticated physical modeling to address non-equilibrium at the wall.