Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography

双曲形式下Serre-Green-Naghdi方程的半隐式策略：双曲松弛真的是个好主意吗？

Semi-implicit strategies for the Serre-Green-Naghdi equations in hyperbolic form. Is hyperbolic relaxation really a good idea?

针对Serre-Green-Naghdi方程椭圆形式计算成本高的问题，提出双曲模型（hSGN）的半隐式积分策略，在IMEX Runge-Kutta框架内隐式处理刚性项、显式处理平流分量，缓解稳定性约束并保持精度，为经典SGN和全显式hSGN求解器提供高效准确替代方案。

A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies

We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to overcome the numerical difficulties and the severe time step restrictions arising from higher order terms. The proposed model reduces to the original SGN model when an artificial sound speed tends to infinity. Moreover, it is endowed with an energy conservation law from which the energy conservation law associated with the original SGN model is retrieved whe…

Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations

We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre-Green-Naghdi system; it describes future states of the free water surface and depth averaged horizontal velocity, given their initial state. The lack of knowledge of the velocity field as well as the initial states provided by measurements lead to an ill-posed problem that cannot be solved by traditional techniques. To this end, we employ physics-informed neural networks (PINNs) to generate solutions to such ill-posed problems using only data of the free surface…

Serre-Green-Naghdi 方程的预处理与线性隐式时间积分

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations

本文为 SGN 方程提出常系数预处理器并证明条件数界，结合显式与线性隐式时间积分，实现高效求解含地形孤立波问题。

使用Green-Naghdi模型对强非线性和色散波进行数值模拟

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

本文研究Green-Naghdi模型在强非线性和色散波传播中的能力，通过改进的混合有限体积-有限差分分裂方法，在淹没沙洲波浪传播基准测试中取得了令人满意的结果。

用于色散海啸传播的隐式自适应网格细化

Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation

本文提出在GeoClaw中基于块自适应网格细化隐式求解Serre-Green-Naghdi色散方程，以提升短波长海啸建模的精度与稳定性。

Hamiltonian regularisation of shallow water equations with uneven bottom

The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a so-called Hamiltonian regularisation for nonlinear shallow water and isentropic Euler equations. The characteristic property of this method is that the regularisation of solutions is achieved without adding any artificial dissipation or ispersion. The regularised system possesses a Hamiltonian structure and, thus, formally preserves the corresponding energy f…

自适应、高效且可扩展的色散双曲系统水波建模

Adaptive, efficient, and scalable water wave modeling with dispersive hyperbolic systems

提出一种结合色散双曲模型与浅水方程的方法，利用自适应网格细化和共享内存并行，在GeoClaw中实现，相比现有色散求解器加速约2倍。

High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves

In this paper, we propose a unified and high order accurate fully-discrete one-step ADER Discontinuous Galerkin method for the simulation of linear seismic waves in the sea bottom that are generated by the propagation of free surface water waves. A hyperbolic reformulation of the Serre-Green-Naghdi model for nonlinear dispersive free surface flows is coupled with a first order velocity-stress formulation for linear elastic wave propagation in the sea bottom. Cartesian non-conforming meshes are defined and the coupling is achieved by an appropriate time-dependent pressure boundary condition in …