Adjoint-based calibration of nonlinear coupled constitutive relations for argon normal shocks with a differentiable finite-volume solver

Qirong Tu; Mengjia Wu; Gaoxiang Xiang

doi:10.54097/tb059w44

Authors

Qirong Tu School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
Mengjia Wu School of Mechanics and Transportation Engineering, Northwestern Polytechnical University, Xi’an 710129, People’s Republic of China
Gaoxiang Xiang School of Mechanics and Transportation Engineering, Northwestern Polytechnical University, Xi’an 710129, People’s Republic of China

DOI:

https://doi.org/10.54097/tb059w44

Keywords:

Nonlinear coupled constitutive relations; argon normal shocks; parameter calibration; discrete adjoint; differentiable finite-volume solver.

Abstract

Nonlinear coupled constitutive relations (NCCR) extend the Navier–Stokes–Fourier equations through nonlinear dissipation and stress–stress and heat-flux–stress couplings. We calibrate their three constants for argon normal shocks using an implicit constitutive layer, a differentiable finite-volume solver and a discrete adjoint. A phase condition removes the translational mode of the steady shock. With the viscosity law and Prandtl number fixed, joint calibration at Mach 2.05–8 gives and reduces the density–temperature misfit by 86.8%. The Mach-8 heat-flux peak underprediction falls from 21.4% to 6.7%. The enhanced heat-flux–stress coupling persists after recalibration with each training Mach number omitted in turn and with independent DS1V data. Strong shocks drive the dissipation scale to zero, whereas weak shocks constrain it poorly. The upstream temperature precursor remains too short, limiting extrapolation beyond the fitted one-dimensional compression flows.

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