A consistent quasi–second-order staggered scheme for the two-dimensional shallow water equations

Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators height and momentum balance performed order improve accuracy scheme. time either by first-order segregated forward Euler or second-order Heun Both schemes shown preserve positivity under Courants Friedrichs Lewy (CFL) condition an important state equilibrium known as lake at rest. Using some recent Lax–Wendroff type results grids, these be LW-consistent weak formulation continuous equations, sense that if sequence bounded strongly converges limit, then this limit solution SWEs; besides, entropy inequality. Numerical confirm efficiency schemes.