Numerical Solution of the Advection Equation with Periodic Boundary Conditions using the FTCS Method

Abstract

In this paper, we considered the advection partial differential equation, a fundamental model in fluid dynamics and various other disciplines, exploring its numerical solutions, which hold significant importance across its applications. We consider a numerical method, such as finite difference method particularly forward in time and central in space methods (FTCS) for the solution of PDE, and also checked the stability condition while solving the advection partial differential equation. In this case, we took a one-dimensional scenario with periodic boundary conditions, scrutinizing the accuracy and stability across varying velocity, spatial, and time dependent parameters. We further examine the impact of spatial and temporal resolutions on method stability and offer practical insights for selecting appropriate numerical values and parameters for optimal advection equation solutions. A code in MATLAB is derived for simulation and graphical results are given in the paper.

Keywords: Advectionpartial Differential Equation, Periodic Boundary Conditions, Finite Difference Method