Most parallel and distributed platforms available today show a large unbalance between slow communications and fast local computations which makes the scheduling of tasks much harder to handle efficiently. The so called scheduling with large communication delays problem has been proved to be NP-hard even in some restricted cases. Its status regarding approximation is still unknown. In this work, we propose to study this challenging problem for graphs with a specific structure of 2-dimensional grids. More precisely, we provide lower and upper bounds for both sub-problems of unbounded number of processors and two processors. We show in both cases that the proposed scheduling algorithms are close to lower bounds.