An Undecomposed Hybrid Algorithm for Nonlinear Coupled Constitutive Relations of Rarefied Gas Dynamics

Jiang, Zhongzheng

doi:10.4208/cicp.oa-2018-0056

Cited by 25 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eu [12] proposed generalized hydrodynamic equations (GHE) from a different viewpoint in 1992 and developed nonlinear coupled constitutive relations (NCCR) with Myong [13,14] based on GHE subsequently. As a simplified approximation of GHE, NCCR includes the evolution equations of conservative variables and nonlinear coupled closure of stress tensor and heat flux, which is strictly consistent with the second law of thermodynamics [15]. Except DSMC, Boltzmann equation and moment equation solvers, many coupling models have also been proposed recently such as traditional CFD-DSMC hybrid method [16], unified gas-kinetic wave-particle method (UGKWP) [17], general synthetic iterative scheme (GSIS) [18], unified stochastic particle method based on the BGK model (USP-BGK) and simplified unified wave-particle method (SUWP) [20].…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Nonlinear Constitutive Relations for Rarefied Flow Computations

Zhao

Jiang

Yao

et al. 2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Data-Driven Nonlinear Constitutive Relations for Rarefied Flow Computations

Zhao

Jiang

Yao

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Eu [12] proposed generalized hydrodynamic equations (GHE) from a different viewpoint in 1992 and developed nonlinear coupled constitutive relations (NCCR) with Myong [13,14] based on GHE subsequently. As a simplified approximation of GHE, NCCR includes the evolution equations of conservative variables and nonlinear coupled closure of stress tensor and heat flux, which is strictly consistent with the second law of thermodynamics [15]. Except DSMC, Boltzmann equation and moment equation solvers, many coupling models have also been proposed recently such as traditional CFD-DSMC hybrid method [16], unified gaskinetic wave-particle method (UGKWP) [17], general synthetic iterative scheme (GSIS) [18], unified stochastic particle method based on the BGK model (USP-BGK) [19] and simplified unified wave-particle method (SUWP) [20].…”

Section: Introductionmentioning

confidence: 99%

Data-driven nonlinear constitutive relations for rarefied flow computations

et al. 2021

View full text Add to dashboard Cite

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 first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases 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 various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.

show abstract