Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Comparison of a Material Point Method and a Galerkin meshfree method for the simulation of cohesive-frictional materials

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literature are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences fromPeer ReviewedPostprint (published version

Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces

We study the non-linear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, we apply the {\it closure approximation} that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and non-linear propagator. The resultant integral expressions keep important non-perturbative properties which can dramatically improve the prediction of non-linear power spectrum. Employing the Born approximation, we then derive the analytic expressions for non-linear power spectrum and the predictions are made for non-linear evolution of baryon acoustic oscillations in power spectrum and correlation function. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of non-linear redshift-space distortion, we also evaluate the power spectrum and correlation function in correlation function. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3 at z>=0.5.Comment: 25 pages, 15 figures, accepted for publication in Phys.Rev.