Finite Volume Method: An Efficient Tool for Transport Equation Solutions

Abstract

A strong and flexible numerical method for solving transport equations encountered in various scientific and engineering applications is the Finite volume method (FVM). The free-volume model (FVM) provides a strong basis for modeling the advection-dominated transport phenomena by partitioning the domain into control volumes and applying the conservation rules here. Focusing on its efficiency and accuracy, this paper delves into the basic concepts of the FVM and how it is applied to solve transport equations. Topics covered include numerical flux formulas, consideration of boundary conditions, spatial and temporal discretization techniques, and other important details. We prove that the technique can capture both continuous and discrete solutions to complicated transport phenomena by thoroughly analyzing its benefits. Our numerical findings show that the Finite Volume Method is useful in solving many kinds of transport equations, and they come from real-world applications. We highlight the method's flexibility to handle various problem situations and its ability to improve computational performance through parallel computing. While exploring the Finite Volume Method's potential, we take into account the factors that could affect its implementation. We go over current innovations and those on the horizon, pointing out places where things could be optimized and improved. In order to help researchers, engineers, and practitioners in their fields who are looking for efficient computational methods to simulate transport phenomena with reliable results, this study aims to give a brief but thorough overview of the FVM.