Cross-Model Verification of Wall-Bounded Flows using Finite-JAX

Abstract

Accurate prediction of wall-bounded flows remains central to advancing both theoretical understanding and computational methods in fluid mechanics. In this study, we perform a numerical simulation of channel flow using a complementary approach: a high-performance, differentiable finite-difference solver developed in JAX (Finite-JAX), and an analytical solution derived from the Navier-Stokes Equations, also known as the Hagen-Poiseuille equation. The solver is applied to the incompressible Navier-Stokes equations, along with appropriate boundary conditions, to capture canonical flow features, including velocity profiles and pressure gradients. Cross-model verification is conducted by systematically comparing numerical results between Finite-JAX and the analytical solution, with a focus on velocity distributions. In addition, numerical results are benchmarked against analytical solutions for the laminar regime, allowing direct quantification of the verification accuracy. Our findings demonstrate that cross-model verification not only strengthens confidence in simulation fidelity but also provides a pathway for integrating differentiable solvers with established computational fluid dynamics platforms, paving the way for future fluid flow research. The performance of Finite-JAX on Wall-Bounded Flows is 0.014765 in the L2 norm.