Anisotropic deep learning transport models for two-dimensional transition-continuum flows

In order to simulate rarefied and non-equilibrium flows accurately, the Boltzmann equations are typically used, but they are computationally expensive and provide only approximate solutions. The Navier-Stokes equations, which are computationally tractable, become unreliable in these regimes due to their reliance on the continuum assumption. To address this, a recent study introduced a deep learning framework that augments the Navier-Stokes equations to accurately predict normal shocks in transition-continuum flow regimes [1, 2]. This framework incorporates known Navier-Stokes physics and ensures consistency with the forward equations, while also applying entropy constraints on the closure model outputs to maintain compliance with the second law of thermodynamics. The deep neural network is trained using adjoint equations, which calculate the loss sensitivities with respect to the dependent variables. Three augmented models and a slip-wall boundary condition model are compared, demonstrating the framework’s effectiveness on two-dimensional shock cases.