Journal of Engineering Mathematics & Statistics

Authors: Snehal Joshi, Amit Nath

Abstract: The study of fluid flow is crucial in various engineering applications, such as in aerospace, civil, mechanical, and chemical engineering. Numerical methods provide an efficient way to analyze and solve complex fluid flow problems that cannot be solved analytically. Among these methods, the Finite Element Method (FEM) has gained significant importance due to its ability to handle complex geometries, boundary conditions, and varying material properties. This paper aims to explore the numerical modeling of fluid flow using advanced finite element methods, focusing on the implementation, applications, and optimization techniques. The research also delves into the role of computational fluid dynamics (CFD) and the integration of FEM with turbulence models. Various case studies and examples are provided to demonstrate the efficiency and accuracy of the method. Additionally, challenges in numerical stability, convergence, and computational cost are discussed along with potential solutions.

Keywords: Finite Element Method (FEM), Fluid Flow, Computational Fluid Dynamics (CFD), Numerical Modeling, Turbulence Models, Fluid Mechanics, Mesh Generation, Convergence, Stability, Optimization.