Related papers: Stable and high-order accurate finite difference m…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
In many applications, and in particular in seismology, realistic propagation media disperse and attenuate waves. This dissipative behavior can be taken into account by using a viscoacoustic propagation model, which incorporates a complex…
In this work, we study two-dimensional diffusion-wave equations with variable exponent, modeling mechanical diffusive wave propagation in viscoelastic media with spatially varying properties. We first transform the diffusion-wave model into…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly along a conduit of a viscous liquid. Formally, the behavior of modulated periodic waves on large space and time scales may be…