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

Arturo Rodriguez; Avinash Potluri; Aryan Singh; Vyom Kumar; Kate Reza; Francisco O. Aguirre Ortega; Vineeth Vijaya Kumar; Noah L. Estrada

arXiv · 2509.25569

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

Arturo Rodriguez·Avinash Potluri·Aryan Singh·Vyom Kumar·Kate Reza·Francisco O. Aguirre Ortega·Vineeth Vijaya Kumar·Noah L. Estrada

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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.

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Arturo Rodriguez, Avinash Potluri, Aryan Singh, Vyom Kumar, Kate Reza, Francisco O. Aguirre Ortega, Vineeth Vijaya Kumar, Noah L. Estrada. 2025-12-17. Cross-Model Verification of Wall-Bounded Flows using Finite-JAX. https://arxiv.org/abs/2509.25569

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