相关论文: A new run-up algorithm based on local high-order a…

The evolution of breaking waves propagating towards the shore and more specifically the run-up phase over the swash-zone for surface as well as for internal waves is considered. The study is based on a) laboratory run up experiments for…

The problem of tsunami wave run-up on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the run-up characteristics for various shapes of the incoming symmetrical…

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…

Numerous codes are being developed to solve Shallow Water equations. Because they are used in hydraulics and environmental studies, their capability to simulate properly flow dynamics is essential to guarantee infrastructure and human…

The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…

Reduced models for free-surface flows are required due to the high dimensionality of the underlying incompressible Navier-Stokes equations, which need to fully resolve the flow in vertical direction to compute the surface height. On the…

The manuscript presents a new technique for computing the exponential of skew-Hermitian operators. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many…

The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial conditions pose significant challenges, often leading to a…

In this study, a numerical model preserving a class of nontrivial steady-state solutions is proposed to predict waves propagation and waves run-up on coastal zones. The numerical model is based on the Saint-Venant system with source terms…

We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…

We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…

Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising…

The classical dam break problem has become the de facto standard in validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is…

The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…

When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…

A new algorithm, denoted by RSRR, is presented for solving large-scale nonlinear eigenvalue problems (NEPs) with a focus on improving the robustness and reliability of the solution, which is a challenging task in computational science and…

We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the…

The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…