Ankit Awasthi
Mathematics
Janurary 2025
Nonlinear partial differential equations (PDEs) are the core of fluid dynamics, describing complex fluid systems' behavior in diverse applications. In most cases, analytical solutions to these nonlinear PDEs are impossible due to the inherent nonlinear and chaotic behavior of fluid motion, and hence numerical methods have to be applied. These will explore the numerical schemes such as FDM, FEM, Spectral Methods, and Mesh-Free Methods with regard to their feasibility in fluid dynamics while providing an approximation for nonlinear PDEs using the challenges they overcome regarding the issues of turbulence, complex geometry, and dynamical conditions on the boundaries. The discussion also underscores real-world applications, such as turbulence modeling, weather forecasting, and industrial process optimization, making the transformative role of numerical methods in advancing fluid dynamics research and practice clear
17- 29
© Airo Journals 2021
