This article presents a two dimensional macroscopic model for traffic flow on a network. We consider a two dimensional conservation law where we suggest a new method to estimate the direction of the velocity using only information and properties of the network. We present an algorithm for the computation of the two dimensional velocity on the network and present numerical simulations. Moreover, the numerical approximation of the two dimensional equation is carried out using an operator and splitting method and we present the results of some simulations on some realistic network. Lastly, we propose a comparison with the well-known CTM method.