Simulation of Long Waves in Branching Waterways

The system is divided into overlapping segments and the motion is computed for each segment separately over a time increment short enough to ensure that errors due to neglect of neighboring segments are confined to the regions of overlap. The solution for the whole system at the end of each time increment is found by discarding erroneous portions of the solutions for the various segments and piecing together the remaining parts. The difficulties of programming a single large difference scheme to cover a whole inlet or river are avoided and the problem is reduced to linking standard subroutines representing commonly-encountered features such as bifurcations and confluences. The results are presented for a numerical experiment designed to test the method in a known physical situation and to compare various methods of linking adjacent segments.