The ambisonics format is a powerful audio tool designed for spatial encoding of the pressure field. An under-exploited feature of this format is that it can be directly extracted from virtual acoustics simulations. Finite Difference Time Domain (FDTD) simulations are particularly adapted as they simplify greatly the problem of extracting spatially-encoded signals, and enable real-time processing of the simulated pressure field. In this short contribution, we first write a time domain representation of the ambisonics channels, in terms of spatial derivatives of the acoustic field at the receiver location, and formulated as a set of ordinary differential equations. We show that in general, the natural corresponding discrete recursive integration yields a prohibitive polynomial drift in time. We then describe a real-time filtering strategy which stabilizes this numerical integration; in the discrete-time setting of FDTD simulations, this real-time filtering process features very low computational costs, avoiding the latency associated with large convolutions and frequency-domain block processing of previous approaches.