Related papers: A Numerical Method for the Two Layer Shallow Water…
We present an advection-pressure flux-vector splitting method for the one and two- dimensional shallow water equations following the approach first proposed by Toro and V\'azquez for the compressible Euler equations. The resulting…
In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry:…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
A numerical method for processing the data of ground penetrating radars for a piece-wise continuous layered medium is proposed. The method combines the layer stripping technique with numerical continuation of data into the complex…
The present paper deals with the modelling of rapid transients at partially lifted sluice gates from both a mathematical and numerical perspective in the context of the Shallow water Equations (SWE). First, an improved exact solution of the…
Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite…
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
In this paper, we propose a novel approach for controlling surface water waves and their interaction with floating bodies. We consider a floating target rigid body surrounded by a control region where we design three control strategies of…
This paper presents the numerical solution of immiscible two-phase flows in porous media, obtained by a first-order finite element method equipped with mass-lumping and flux up-winding. The unknowns are the physical phase pressure and phase…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
A numerical method is described for studying how elastic waves interact with imperfect contacts such as fractures or glue layers existing between elastic solids. These contacts have been classicaly modeled by interfaces, using a simple…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…