• urban drainage;
  • semi-implicit method;
  • mildly nonlinear system;
  • free surface flow;
  • pressurized flow;
  • shallow water;
  • wetting and drying


In this paper, a semi-implicit numerical model for one-dimensional urban drainage networks is formulated in such a fashion as to intrinsically account for arbitrary cross sections, for the occurrence of dry areas, for free surface, and for pressurized flows. The governing differential equations are discretized with a consistent mass conservative scheme that naturally applies to all flow regimes. The resulting mildly nonlinear system, at every time step, is efficiently solved with a converging, properly devised, nested Newton-type algorithm. It will be shown that with the proposed semi-implicit model, high accuracy can be achieved at a moderate computational cost. Copyright © 2013 John Wiley & Sons, Ltd.