Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking (Journal of Mathematical Study, 2022)
In this paper, we propose a spectral projection of a regularized Boussinesqsystem for wave propagation on the surface of a fluid. The spectral method is basedon the use of Legendre polynomials, and is able to handle time-dependent Dirichletboundary conditions with spectral accuracy.The algorithm is applied to the study of undular bores, and in particular to the onsetof wave breaking connected with undular bores. As proposed in [2], an improvedversion of the breaking criterion recently introduced in [5] is used. This tightenedbreaking criterion together with a careful choice of the relaxation parameter yieldsrather accurate predictions of the onset of breaking in the leading wave of an undularbore.
Keywords: Boussinesq system; Legendre projection; undular bore; wave breaking; boundary conditions; spectral accuracy.