Explosive solar activities cause heliospheric disturbances. A simple scheme of simulating the propagation of shock waves in the heliosphere is devised to study such disturbances caused by solar flares. This scheme, the HAF scheme, is capable of simulating the propagation of many shock waves generated during extended periods up to a distance of 100 au (200 days) during periods when many solar disturbances can occur. The capability of the scheme is demonstrated in reproducing: (1) Multi-events with multi-satellite data within 2 au: (2) The heliospheric conditions at Ulysses/ Cassini within 10 au. (3) A successful reproduction of a Pioneer 11 event at 30 au. (4) The heliospheric condition up to 100 au in 2004, in addition to (5) reproducing recurrent geomagnetic srorms. Thus, the method presented here is simple enough in predicting a rough overall pattern of heliospheric disturbances on a day-to-day basis without MHD simulations. In this paper, we assembled systematically (in terms of distance from the sun) the above multiple results during the development of the HAF scheme in different periods by many researchers. It is hoped that much better schemes will be developed by extending and improving the HAF scheme.