A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem

Abstract

This paper is concerned with the development of a formulation of the Finite Difference Method, in the solution of the transient diffusion-advection equation. In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. This integration reduces the order of time derivative in the basic equation and the initial conditions can be taken into account directly in consequence. Three pollutant transport problems are presented in order to verify the stability and accuracy of the proposed approach. The results for this approach are compared with the Boundary Element Methods results. The comparisons of numerical results show a good agreement between the furnished results for the proposed approach and the boundary element method results assumed here as reference results. By analyzing the results one can conclude that the formulation presented in this paper is capable of producing accurate results for the problem.