On the Numerical Solution of Advection-Diffusion Problems with Singular Source Terms

Abstract

A numerical study is presented of 1D advection-diffusion problems having singular source terms. The singular source terms are defined by a Dirac delta function. As a consequence, the solutions of such problems are not continuously differentiable. This lack of smoothness form an obstacle for numerical discretization, including amongst others order reduction. In this paper the standard finite volume approach is considered for which reduction from order two to order one occurs. Numerical example is included.