This article highlights a study focused on resolving a nonlinear problem in fluid dynamics using the Navier–Stokes equations as a mathematical model. The study focuses on comparing the isogeometric analysis (IGA) B-spline method with the traditional finite element method (FEM) in a two-dimensional context. The objective is to showcase the superior performance of the IGA method in terms of result quality and computational efficiency. The study employs GEOPDE’s MATLAB code for implementing and computing the NURBS method and COMSOL Software’s FEM code for comparison. The advantages of the IGA B-spline method are highlighted, including its ability to accurately capture complex flow behavior and its reduced computation time compared to FEM. The study aims to establish the superiority of the IGA method in solving nonlinear Navier–Stokes equations, providing valuable insights for fluid dynamics and practical implications for engineering simulations.

In this research, an attempt was made to employ the Non-Uniform Rational B-Splines (NURBS) method for a challenging computational fluid dynamics (CFD) problem of aerodynamics around NACA 2412 airfoils. The comparison was carried out thoroughly by using the same boundary conditions and geometry, comparing NURBS to standard FEM implementations. Our study was interested in demonstrating the foreseeable functionalities of NURBS for solving complex CFD problems and conducting a comparative effectiveness performance evaluation between them with traditional FEM methodologies.