Data-driven nonlinear constitutive relations for rarefied flow computations

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