Reliability of first order numerical schemes for solving shallow water   system over abrupt topography
  We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed error depends on the method. Moreover, the solutions given by the numerical scheme can be significantly different if not enough space resolution is used. We shall pay special attention to the well-known hydrostatic reconstruction technique where it is shown that large bottom discontinuities may be neglected and a modification is proposed to avoid this problem. 
T. Morales de Luna and M.J. Castro D\'iaz and C. Par\'es Madro\~nal
math.NA