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 referred to 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 such as 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 laminar regimes, allowing for the direct quantification of verification accuracy errors. 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.

翻译：壁面约束流动的精确预测对于推进流体力学理论理解和计算方法的发展至关重要。本研究采用互补方法对槽道流动进行数值模拟：一种是基于JAX开发的高性能可微有限差分求解器（Finite-JAX），另一种是从Navier-Stokes方程导出的解析解（亦称为Hagen-Poiseuille方程）。该求解器应用于不可压缩Navier-Stokes方程及相应的边界条件，以捕捉速度剖面和压力梯度等典型流动特征。通过系统比较Finite-JAX数值解与解析解的速度分布，开展了跨模型验证研究。此外，数值结果在层流工况下与解析解进行基准对比，实现了验证精度误差的直接量化。研究结果表明，跨模型验证不仅能增强对模拟保真度的置信度，还为可微求解器与现有计算流体动力学平台的集成提供了途径，为未来流体流动研究开辟了新道路。