Numerical Solution of Advection-Diffusion Equation Using Operator Splitting Method

Abstract

In this study, effects of operator splitting methods to the solution of advection-diffusion equation are examined. Within the context of this work two operator splitting methods, Lie-Trotter and Strang splitting methods were used and comparisons were made through various Courant numbers. These methods have been implemented to advection-diffusion equation in one-dimension. Numerical solutions of advection and dispersion processes were carried out by a characteristics method with cubic spline interpolation (MOC-CS) and Crank-Nicolson (CN) finite difference scheme, respectively. Obtained results were compared with analytical solutions of the problems and available methods in the literature. It is seen that MOC-CS-CN method has lower error norm values than the other methods. MOC-CS-CN produces accurate results even while the time steps are great.