We present a new powerful tool to simulate the streamer belt of the solar corona based on forward modeling. It takes into account the temporal evolution of the corona and provides both qualitative and quantitative results. Starting from the National Solar Observatory photospheric magnetograms, the position of the neutral line at the source surface (2.5 Rsun) is caculated using the potential field source surface model. The plasma sheet of the streamer belt is centered around the current sheet represented as the radial extension of the neutral line. The 3D electron density is represented with octree compression and the radiance images are computed by a ray-tracing algorithm implementing the Thomson scattering. A multi-octree method allows to simulate the temporal evolution of the streamer belt and to compute the synoptic maps from time-series of generated images. The comparison between the synoptic maps of the streamer belt obtained with the SOHO/LASCO-C2 coronagraph and the simulated synoptic maps constructed from our model shows a global agreement for both radiance profiles and global behaviour of the streamer and confirms earlier findings by Wang et al. (1997) that the streamers are associated with folds in the plasma sheet. However, some features cannot be explained using this method and are interpreted by introducing two types of large-scale structures. Our results suggest that the potential field source surface model is not fully adequate for the description of the fine structure of the streamer belt, even during the time of low solar activity. We present new applications of our method to future coronographic observations with SECCHI/COR-2 on STEREO and SILC on Solar Orbiter.