• Tue. Feb 11th, 2025

SSAR Publishers

Scholar Scientific and Academic Research Publishers

Numerical Solution of Incompressible Navier-Stokes Equations and Applications

ABSTRACT: The Navier-Stokes equations are nonlinear partial differential equations that serve as fundamental equations governing the fluid flow. Owing to this nonlinearity, analytical methods often fail to find solutions; hence, there is a demand for numerical methods to approximate the results. Therefore, we used the finite volume method to determine its solutions numerically. In this note, we conducted a study to solve these problems using the finite volume method. Our objective is to develop a numerical algorithm that is tailored to discretize the Navier-Stokes equations using the finite volume method. Subsequently, we implemented the developed numerical algorithm in Python to simulate the two-dimensional flow solutions. Furthermore, we conducted a thorough stability analysis of the algorithm to assess its numerical stability under various grid resolutions, time step sizes, and physical parameters. The anticipated outcome of solving the Navier-Stokes equations using the finite volume method includes obtaining numerical solutions that accurately describe the behavior of fluid flow within a given computational time. The simulations yielded detailed insights into the flow characteristics, including the velocity profiles, pressure distributions, and vorticity patterns. Our findings contribute to the advancement of numerical techniques in computational fluid dynamics.

KEYWORDS: Navier-Stokes equations, Numerical solution, Stability, Finite volume method