[en] Laser-driven acceleration in dielectric structures can provide gradients on the order of GeV/m. The small transverse dimension and tiny feature sizes introduce challenges in design, fabrication, and simulation studies of these structures. In this paper we present the results of beam dynamic simulation and short range longitudinal wakefield simulation of the double grating structure. We show the linear trend of acceleration in a dielectric accelerator design and calculate the maximum achievable gradient equal to 0.47E₀ where E0 is maximum electric field of the laser excitation. On the other hand, using wakefield simulations, we show that the loss factor of the structure with 400nm gap size will be 0.12GV/m for a 10fC, 100as electron bunch which is an order of magnitude less than expected gradient near damage threshold of the device.