Cross-Model Verification of Wall-Bounded Flows using Finite-JAX
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arXiv
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| Format: | Preprint |
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2025
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| author | Rodriguez, Arturo Potluri, Avinash Singh, Aryan Kumar, Vyom Reza, Kate Ortega, Francisco O. Aguirre Kumar, Vineeth Vijaya Estrada, Noah L. |
| author_facet | Rodriguez, Arturo Potluri, Avinash Singh, Aryan Kumar, Vyom Reza, Kate Ortega, Francisco O. Aguirre Kumar, Vineeth Vijaya Estrada, Noah L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cross-Model Verification of Wall-Bounded Flows using Finite-JAX Rodriguez, Arturo Potluri, Avinash Singh, Aryan Kumar, Vyom Reza, Kate Ortega, Francisco O. Aguirre Kumar, Vineeth Vijaya Estrada, Noah L. Fluid Dynamics Numerical Analysis 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. |
| title | Cross-Model Verification of Wall-Bounded Flows using Finite-JAX |
| topic | Fluid Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2509.25569 |