Entropy-Compatible Reconstruction for High-Weissenberg Viscoelastic Flow

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.