### A numerical solution for advection-diffusion equation based on a semi-Lagrangian scheme

Ersin Bahar, Sıla Övgü Korkut, Yeşim Çiçek, Gürhan Gürarslan

#### Öz

This paper describes a numerical solution for the advection-diffusion equation.  The proposed method is based on the operator splitting method which helps to obtain accurate solutions.  That is, instead of sum, the operators are considered separately for the physical compatibility.  In the process, method of characteristics combined with cubic spline interpolation and Saulyev method are used in sub-operators, respectively.  After guaranteeing the convergence of the method the efficiency is also tested on one-dimensional advection-diffusion problem for a wide range of Courant numbers which plays a crucial role on the convergence of the solution.  The obtained results are compared with the analytical solution of the problem and other solutions which are available in the literature.  It is revealed that the proposed method produces good approach not only for small Caurant numbers but also big ones even though it is explicit method.

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