Efficient Numerical Approaches for Solving Navier-Stokes Equations in Computational Fluid Dynamics

Abstract
The Navier-Stokes Equations (NSE) are central to fluid dynamics, defining the dynamics of
fluid flow. Nevertheless, their solution, especially for turbulent flows, is still computationally
expensive. Conventional numerical schemes such as the Finite Volume Method (FVM) are
highly accurate but come at the cost of heavy computational loads. Conversely, deep-learningbased methods like the Fourier Neural Operator (FNO) offer computational efficiency but lack
accuracy and stability in intricate flow conditions. This work presents a hybrid numerical
scheme that combines FVM and FNO to achieve a balance between computational efficiency
and accuracy. The hybrid method utilizes FVM for high-fidelity discretization and FNO for
fast solution approximation, with an adaptive correction process to maintain numerical
stability. The findings prove that the Hybrid FVM-FNO approach reduces computation time
considerably with accuracy comparable to traditional solvers. Comparative results indicate that
this hybrid approach achieves a 3× speedup compared to FVM with very high accuracy and is
thus capable of real-time fluid simulation. This method has far-reaching implications in
computational fluid dynamics (CFD) simulations, such as aerospace, weather forecasting, and
biomedical flow studies