Analysis and Computation with Stratified Fluid Models

Abstract

Vertical averaging of the three-dimensional incompressible Euler equations leads to several reduced dimension models of flow over topography, including the one-layer and two-layer classic shallow water equations, and the one-layer and two-layer nonhydrostatic Green–Naghdi equations. These equations are derived and their well-posedness is discussed. Several implicit and explicit finite difference approximations of both the shallow water and Green–Naghdi models are presented, but for Green–Naghdi these are obtained using automatic code generation software. Numerical results are given in both well-posed and ill-posed regimes and compared with computations obtained by others.