  In this paper we propose high order numerical methods to solve a 2D
advection-diffusion equation, in the highly oscillatory regime. We use an
integrator strategy that allows the construction of arbitrary high-order
schemes which leads to an accurate approximation of the solution without any
time step-size restriction. This paper focuses on the time multiscale challenge
of the problem, that comes from the velocity, an epsilon-periodic function,
whose expression is explicitly known. epsilon-uniform third order in time
numerical approximations are obtained. For the space discretization, this
strategy is combined with high order finite difference schemes. Numerical
experiments show that the proposed methods achieve the expected order of
accuracy.
