An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation

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Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up (2009, methodology): “Overall, the upwind flux approximation (13a and 13b) and the second-order scheme (15a and 15b) in the present model provide the same or slightly better results compared with Stelling and Zijlema [12] and Walters [15].”
Shock-capturing non-hydrostatic model for fully dispersive surface wave processes (2012, methodology): “To address this issue, Stelling and Zijlema (2003) proposed the Keller-box method to replace the staggered grid in the vertical direction, which enables the pressure to be located at the cell faces rather than the cell centers.”
Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure (2008, methodology): “As a whole, the numerical models of Stelling and Zijlema (2003) and Zijlema and Stelling (2005) represent a good balance between nonlinearity (enables wave shoaling) and frequency dispersion (corrects celerity of shoaling wave) so that initiation of the wave breaking process and the associated…”
Depth‐integrated, non‐hydrostatic model with grid nesting for tsunami generation, propagation, and run‐up (2010, background): “Zijlema and Stelling [22] and Yamazaki et al. [17], respectively, applied the momentum-conserved advection scheme in a two-layer and a depth-integrated non-hydrostatic model for breaking of dispersive waves with encouraging results.”