(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Numerous numerical solutions have been developed over the past decades to provide suitable solutions for several types of problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique adopted in computational fluid dynamics to solve partial differential equations representing conservation laws. In this article, two mathematical models are presented: one for the linear advection equation and another for the nonlinear Burgers’ equation with diffusion, along with various schemes of the FVM. Furthermore, numerical experiments will be conducted for several FVM schemes to demonstrate the most effective approach for solving the studied problem.