High-precision Euler wavelet methods for fractional Navier–Stokes equations and two-dimensional fluid dynamics

Numerical methods for solving fractional Navier–Stokes equations have garnered substantial interest due to their critical role in modeling fluid dynamics. This paper introduces a novel numerical approach that employs the Euler wavelet collocation method to solve the two-dimensional (2D) incompressible stationary flow Navier–Stokes equation with extraordinary accuracy, achieving an absolute error of less than 10−200. While our earlier examples focused on standard boundary conditions, we now emphasize the adaptability of the Euler wavelet method to more complex geometries, such as those encountered in practical applications. This adaptability extends to cylindrical and spherical coordinate systems, allowing for the accurate representation of various fluid flow scenarios. By providing detailed numerical examples that incorporate complex boundary conditions and geometrical considerations, we demonstrate the robustness and effectiveness of the Euler wavelet collocation method. These findings underscore the method's potential as a powerful tool for tackling intricate fluid dynamics challenges across diverse fields requiring high precision in simulations.