2025, Vol. 6, Issue 2, Part C
Numerical analysis of partial differential equations for fluid flow based finite volume methods
Author(s): Dana Tahseen Abdulrahman
Abstract: The finite volume method, or the volumetric approach, is considered one of the most important numerical schemes applied to solve fluid dynamics equations because it keeps physical quantities such as mass, energy, and momentum within the control bodies, especially when applied to the Euler and Navier-Stokes equations and other conservative systems. The book aims to explore the foundations and finite volume methods for solving the fluid mechanics partial differential equations with the goal of finding a balance between accuracy and stability and the conservation of the physical energy, mass, and momentum quantities. It also attempts to describe the importance of these equations in domestic and industrial applications, and how they are most essential in describing the most significant barrier and limitation to their usage, presenting solutions and recommendations through a literature review-based approach by studying 210 associated research papers, narrowed down to 20 studies. One of the most important results of this study is that the finite volume method (FVM) performs extremely well in solving fluid flow PDEs with shocks and sudden property changes. The most significant advantages of the finite volume method are conservation of physical values and flexibility in distorted meshes, making it ideal for complex engineering problems. Godunov and Riemann schemes provide exact solutions in shocks, and ENO/WENO methods improve accuracy for high-scale problems. Novel research directions include higher-order methods and well-balanced schemes for improving stability. High-performance computers (HPC) advances enable developing more extensive and more complex FVM models and amplify their use in industrial simulations and sustainable technology applications.
DOI: https://doi.org/10.22271/math.2025.v6.i2c.251
Pages: 509-515 | Views: 582 | Downloads: 294
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How to cite this article:
Dana Tahseen Abdulrahman. Numerical analysis of partial differential equations for fluid flow based finite volume methods. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(2): 509-515. DOI: 10.22271/math.2025.v6.i2c.251
