The class of affine forward variance (AFV) models was defined in Gatheral and Keller-Ressel (2019); this class includes both the conventional Heston model and its celebrated extension, the rough Heston model of El Euch and Rosenbaum. The AFV characteristic function may be expressed in terms of the solution of a Volterra integral equation. I will present a rational approximation to the solution of this integral equation in the special case of the rough Heston model. Until now, simulation of AFV models using the Markovian approximation of Abi Jaber and El Euch has proved relatively complicated and time-consuming, I will present a new efficient and easy-to-implement method for simulating AFV models for general kernels. I will present numerical results using the rational approximation as a benchmark.