Depth-integrated nonhydrostatic free-surface flow modeling using weighted-averaged equations

In this study, a depth-integrated nonhydrostatic flow model is developed using the method of weighted residuals. Using a unit weighting function, depth-integrated Reynolds-averaged Navier-Stokes equations are obtained. Prescribing polynomial variations for the field variables in the vertical direction, a set of perturbation parameters remains undetermined. The model is closed generating a set of weighted-averaged equations using a suitable weighting function. The resulting depth-integrated nonhydrostatic model is solved with a semi-implicit finite-volume finite-difference scheme. The explicit part of the model is a Godunov-type finite-volume scheme that uses the Harten-Lax-van Leer-contact wave approximate Riemann solver to determine the nonhydrostatic depth-averaged velocity field. The implicit part of the model is solved using a Newton-Raphson algorithm to incorporate the effects of the pressure field in the solution. The model is applied with good results to a set of problems of coastal and river engineering, including steady flow over fixed bedforms, solitary wave propagation, solitary wave run-up, linear frequency dispersion, propagation of sinusoidal waves over a submerged bar, and dam-break flood waves.