Numerical Analysis of Unsteady Incompressible Convection Diffusion Problems Via Finite Volume Method

Abstract

In this study, the Finite Volume Method (FVM) was utilized to solve 2D un steady incompressible convection diffusion problems. FVM is a discretization technique particularly suited for the numerical modeling of numerous conser vation laws that have been widely applied in a variety of fields. The numer ical approximation of the convection-diffusion problem has been performed using an implicit scheme in the temporal direction with an upwind differ encing scheme. Two examples were solved using the method to demonstrate the applicability and effectiveness of FVM. Results from graphs and tables demonstrate that the method produces very accurate and efficient solutions to two-dimensional unstable convection-diffusion problems. Additionally, we used the upwind differencing approach to observe the relationship between the directionality of influence and the flow direction and magnitude of the Peclet number. In this instance, a high Peclet number, highly convection dominated diffusion flow was reported, and the flow’s dependence on down stream places was reduced. In conclusion, the numerical results generated by FVM show that the chosen method ensures the transportiveness property of the flow problems and that the numerical results obtained by our suggested numerical approximates are very close to the exact solution.