Abstract
We present a class of first and second order in space and time relaxation schemes for the shallow water (SW) equations. A new approach of incorporating the geometrical source term in the relaxation model is also presented. The schemes are based on classical relaxation models combined with Runge–Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems with or without the source term present. Copyright © 2003 John Wiley & Sons, Ltd.