Related papers: Finite volume schemes for dispersive wave propagat…
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional…
In this paper we propose finite volume schemes for solving the inviscid and viscous quasi-geostrophic equations on coastal-conforming unstructured primal-dual meshes. Several approaches for enforcing the boundary conditions are also…
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance…
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…
The long-term goal of this work is the development of high-fidelity simulation tools for dispersive tsunami propagation. A dispersive model is especially important for short wavelength phenomena such as an asteroid impact into the ocean,…
In this paper we develop a finite element method for acoustic wave propagation in Drude-type metamaterials. The governing equation is written as a symmetrizable hyperbolic system with auxiliary variables. The standard mixed finite elements…
Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical…
Considered herein is a class of Boussinesq systems of Bona-Smith type that describe water waves in bounded two-dimensional domains with slip-wall boundary conditions and variable bottom topography. Such boundary conditions are necessary in…
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving…
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution…
We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order…
We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions…
We consider the outward-propagating nonlinear concentric water waves within the scope of the 2D Boussinesq system. The problem is axisymmetric, and we derive the slow radius versions of the cylindrical Korteweg - de Vries (cKdV) and…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
A general dispersion-dissipation condition for finite difference schemes is derived by analyzing the numerical dispersion and dissipation of explicit finite-difference schemes. The proper dissipation required to damp spurious…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform…