Cross-stream pressure support and the limits of scalar relaxation in rarefied Poiseuille flow

Abstract

The weak wall-normal pressure variation in pressure-driven rarefied Poiseuille flow is a stringent test of higher-order constitutive models: it is almost invisible in the total-pressure norm, yet it is generated by anisotropic molecular stress. A tangent-form nonlinear coupled constitutive relation (NCCR) reproduces its convex topology, but the physical reason for its quantitative success remains unresolved. We ask whether the constitutive stress relation and reduced streamwise forcing are independently accurate or whether their effects compensate. A direct simulation Monte Carlo (DSMC) campaign is analysed using two-dimensional momentum budgets, a pressure-error norm based on the transverse signal, a matched-outlet-Knudsen comparison and componentwise tests of the pre-elimination NCCR balance. The non-equilibrium wall-normal stress over-supports the measured pressure defect, while streamwise transport of shear stress supplies an opposing correction. The state map, momentum budgets and forcing diagnostics show that neither outlet Knudsen nor outlet Mach number alone organises the pressure amplitude; along the fixed-ratio sequence, rarefaction is accompanied by larger changes in the constitutive diagnostics than in pressure amplitude. The DSMC-inferred stress relation departs from the fixed reduced coefficient, and even the best common scalar closes the dominant shear component far more accurately than the normal components that carry the pressure field. Correcting the coefficient alone can therefore worsen the reconstruction, whereas restoring omitted streamwise-momentum terms reduces the amplitude bias in strongly accelerated cases. The reduced law can remain accurate through stress--momentum compensation, showing that agreement of a weak non-equilibrium observable need not imply correct internal closure mechanics.