Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows

Abstract

In high-Knudsen-number flows nonequilibrium effects become dominant and the use of Navier–Stokes–Fourier equations becomes questionable since they are based on small deviation from local thermodynamic equilibrium. In this paper new hydrodynamic computational models are proposed for modeling gases in the transition regime. They are based on Eu’s generalized hydrodynamic equations and it turns out that they apply in all Mach numbers and satisfy the second law of thermodynamics to every order of approximation. In order to learn more about the new equations a model equation similar to the Burgers’ equation is studied. From this analysis new insight into constitutive relations of various hydrodynamic equations has been gained. In addition, a convergent iterative method for solving the highly nonlinear constitutive equations is developed. Finally, the shock structure and slip flow problems are computed by using high resolution numerical schemes and issues of extending the one-dimensional solver to multidimensional problems are discussed.