Abstract: A Euler-Taylor-Galerkin (ETG) algorithm for advection equation has been introduced. To solve the 2-dimensional problem, a time-splitting technique is employed and a Forester nonlinear filter is used to smooth out ripples and suppress negative value. The two dimensional advection test cases of a cosine hill and a Gaussian hill in a pure rotation velocity field are studied. The impacts of time step and spatial resolution on the accuracy of algorithm are also discussed.