2D Serre-Green-Naghdi Equations over Topography: Elliptic Operator Inversion Method

Abstract

Multidimensional Serre–Green–Naghdi equations are numerically solved by using a natural hyperbolic-elliptic splitting. The hyperbolic step is solved by semidiscret finite volume methods. The elliptic step is related to recovering nonhydrostatic pressure. One-dimensional (1D) and two-dimensional (2D) test problems (i.e., 1D solitary wave propagation, 2D dam-break problem, solitary wave overstep and overhump) are considered.