We present a learning-based dynamics model for granular material manipulation. Inspired by the Eulerian approach commonly used in fluid dynamics, our method adopts a fully convolutional neural network that operates on a density field-based representation of object piles and pushers, allowing it to exploit the spatial locality of inter-object interactions as well as the translation equivariance through convolution operations. Furthermore, our differentiable action rendering module makes the model fully differentiable and can be directly integrated with a gradient-based trajectory optimization algorithm. We evaluate our model with a wide array of piles manipulation tasks both in simulation and real-world experiments and demonstrate that it significantly exceeds existing latent or particle-based methods in both accuracy and computation efficiency, and exhibits zero-shot generalization capabilities across various environments and tasks.