  In this article, we propose a two-grid based adaptive proper orthogonal
decomposition (POD) method to solve the time dependent partial differential
equations. Based on the error obtained in the coarse grid, we propose an error
indicator for the numerical solution obtained in the fine grid. Our new
algorithm is cheap and easy to be implement. We apply our new method to the
solution of time-dependent advection-diffusion equations with the Kolmogorov
flow and the ABC flow. The numerical results show that our method is more
efficient than the existing POD methods.
