A second order numerical method for solving advection-diffusion models

The space–time conservation element and solution element (CE-SE) scheme is a method that improves the well-established methods, like finite differences or finite elements: the integral form of the problem exploits the physical properties of conservation of flow, unlike the differential form. Also, this explicit scheme evaluates the variable and its derivative simultaneously in each knot of the partitioned domain. The CE-SE method can be used for solving the advection-diffusion equation.In this paper, a new numerical method for solving the advection-diffusion equation, based in the CE-SE method is developed. This method increases the spatial precision and it is validated with an analytical solution.