Modeling of nearshore flows by means of the classic nonlinear shallow water equations is reviewed and analyzed with a specific focus on the interdependence between physical phenomena, model equations, and numerical schemes. Numerical benchmarking solutions for coastal applications are summarized. Strengths and limits of the nonlinear shallow water equations to reproduce the fundamental features of coastal flows are illustrated along with indications on needed improvements.
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Brocchini et al. (2008) studied this question.
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