Data-Driven Nonlinear Constitutive Relations for Rarefied Flow Computations

Abstract

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed firstly through machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between discrepancies of stress tensors and heat flux and feature vectors is established after training phase. Through the obtained off-line training model, new test case excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through a various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make DNCR method to be an effective tool in rarefied gas community, especially for hypersonic engineering applications.