Entropy-Compatible Reconstruction for High-Weissenberg Viscoelastic Flow

Abstract

Log-conformation and square-root reconstructions preserve positive definiteness in high-Weissenberg viscoelastic simulations, but positivity alone does not guarantee compatibility with the discrete free-energy balance. We identify three reconstruction-level mechanisms by which strictly positive tensors can still generate nonphysical behavior: Jensen-type entropy bias, exponential amplification of logarithmic perturbations in highly stretched states, and sign-indefinite polymeric-work defects caused by using incompatible tensors in stress work and entropy variables. We formulate an entropy-compatible reconstruction principle and a corrected logarithmic reconstruction selected by a least-damping entropy constraint. The correction is local, positive, computable by bisection, spectrally controlled, and compatible with coupled velocity--pressure--conformation time stepping. We prove existence of the maximal admissible parameter, convexity of the entropy profile along the logarithmic path, a compatible free-energy estimate, a defect-budget estimate for noncompatible reconstructions, asymptotic inactivity on high-order admissible defects, and a conditional high-stretch resolution advantage in log-relative and entropy metrics. Reproducible diagnostics compare logarithmic, square-root, and linear reconstructions and verify the predicted entropy defects, work defects, stress-force errors, and high-Weissenberg accumulation.