Numerical validation of a double-layer boussinesq-type model for highly dispersive and nonlinear waves

A two-layer Boussinesq-type mathematical model has been recently introduced by the authors with the goal of modeling highly nonlinear and dispersive waves (Chazel et al. 2009, Benoit & Chazel 2010). The analysis of this model has previously shown that it possesses excellent linear properties, up to kh = 10 at least, for dispersion, shoaling coefficient and vertical profile of orbital velocities. In the present work a numerical one-dimensional (1DH) version of model is developed based on a finite difference technique for meshing the spatial domain. It is then applied and verified against a set of three one-dimensional (1DH) test-cases for which either numerical or experimental reference results are available: i. nonlinear and dispersive regular waves of permanent form; ii. propagation of regular waves on a trapezoidal bar (laboratory experiments by Dingemans (1994)); iii. shoaling and propagation of irregular waves on a barred beach profile (laboratory experiments by Becq-Girard et al. (1999)). The test-cases considered in this study confirm the very good capabilities of the model to reproduce either exact solutions, high-precision numerical simulations and experimental measurements in a variety of non-breaking wave conditions and types of bottom profiles. Nonlinearity, dispersion and bathymetric effects are well accounted for by the smodel, which appears to possess a rather wide domain of validity while maintaining a reasonable level of complexity.