2026/08/04 by Aytekin Çibik
Physics and Astronomy · Computer Science · Mathematics · #physics.flu-dyn #cs.NA #math.NA
13 pagesö 5 figures. Original research article
arxiv created 2026/08/04 · arxiv updated 2026/08/06
We study a physics-informed neural network (PINN) for the unsteady, two-dimensional incompressible Navier--Stokes equations in which the stiff divergence-free constraint is replaced by an artificial-compressibility (AC) relaxation governed by a single scalar parameter \eps. The relaxation reintroduces a pressure time derivative, converting a differential-algebraic constraint into an ordinary residual that a PINN can minimise directly. On the Taylor--Green vortex, which admits a closed-form unsteady solution, we quantify the effect of \eps: the residual divergence scales as \eps |∂t p|, so larger \eps raises both the divergence and the velocity error, and both decrease monotonically and saturate as \eps is reduced. On the Re=100 cylinder wake the plain forward AC-PINN collapses to the steady symmetric branch and does not reproduce von Kármán shedding; assimilating a few hundred sparse velocity sensors from a boundary-layer-resolved finite-element reference (whose Strouhal number, 0.176, we bring close to the 0.164--0.172 literature band by resolving the separating shear layer, though it remains just above it) recovers the unsteady vortex street to 7% over the wake and its shedding frequency to within 3% of that same reference --- a bound set by the reference's own fidelity rather than an independent validation against the true flow.