Data-driven Rarefied Non-equilibrium Flow Research On Nonlinear Constitutive Equations

With the development of human aerospace industry,near space has gradually become the strategic commanding height of the world's countries.Compared with traditional aerodynamics,the aerodynamics of near space shows complex multiscale non-equilibrium characteristics.The great development of numerical computing theory and computer software and hardware technology has promoted the rapid progress of computational fluid mechanics.A series of mature single-scale numerical simulation calculation methods have been gradually formed for different flow fields such as the continuous flow Navier-Stokes(NS)equation solver and the rarefied flow Direct simulation of Monte Carlo method(DSMC),etc,but these methods still have their own application limitations and their ability to describe multi-scale coexisting flows is inadequate.In recent years,with the further enhancement of computing capabilities,the increasing accuracy of flow field data and the increasing data amount,machine learning methods have emerged in fluid mechanics,especially in the uncertain modeling of complex fluid nonlinear systems,showing great development potential.In this paper,based on the Navier-Stokes(NS)equations for continuous flow and the Unified Gas-kinetic Scheme(UGKS)method for multi-scale flow,a data-driven rarefied flow non-equilibrium nonlinear constitutive equation(DNCR)and its solution method are proposed.This method uses the flow field numerical simulation results of the Navier-Stokes equation and the UGKS method as a data set.Based on the non-equilibrium flow characteristic parameters,the linear heat flow and stress terms of the Navier-Stokes equation are corrected nonlinearly by machine learning.The numerical solution of the rarefied non-equilibrium flow in the state to be predicted is obtained by solving the macro-conservation equation by coupling the data-driven nonlinear constitutive relationship.Compared with the traditional rarefied-transition flow calculation methods,this method has a calculation accuracy that is consistent with UGKS and it can guarantee the calculation efficiency of the same magnitude as the NS equation under typical conditions.The realization of the DNCR method firstly requires program implementation and verification of the Navier-Stokes equation solver and the UGKS method solver.Based on it,the nonlinear regression relationship modeling of heat and stress term and the characteristic parameters of the flow field and the research of the nonlinear modified coupling solving method are carried out.At the same time,in order to improve the accuracy of the regression relationship model,different flow field feature parameter selection methods,different nonlinear regression models and parameter tuning studies are carried out.Finally,the calculation accuracy and efficiency of the DNCR method are preliminarily evaluated with typical non-equilibrium multi-scale flow characteristics cases.The preliminary simulation results show that the data-driven rarefied non-equilibrium flow nonlinear constitutive equation and its calculation method show excellent capabilities in the calculation accuracy and calculation efficiency of multi-scale non-equilibrium flow.It provides a new idea for the future development of rarefied gas dynamics theory and numerical methods.