The Shallow Water Equations

In this Chapter we derive the time-dependent, non-linear two-dimensional shallow water equations on domains with variableBathymetry  bathymetry. Emphasis is given to the assumptions made in the derivation of the equations, so as to make clear their actual range of applicability. The equations are expressed inConservation law conservation-law form, both in Differential form differential form and in Integral formintegral form. The introduced partial differential equations (PDEs) will be the main focus of the rest of this book.