Non-local dispersive model for wave propagation in heterogeneous media: multi-dimensional case

2002 ◽  
Vol 54 (3) ◽  
pp. 347-363 ◽  
Author(s):  
Jacob Fish ◽  
Wen Chen ◽  
Gakuji Nagai
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Dimensional Case ◽  
Dispersive Model ◽  
Non Local

A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales

2000 ◽  
Vol 68 (2) ◽  
pp. 153-161 ◽  
Author(s):  
W. Chen ◽  
J. Fish
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Multiple Scale ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Homogenization Theory ◽  
Temporal Scales ◽  
Spatial And Temporal Scales ◽  
Dispersive Model

A dispersive model is developed for wave propagation in periodic heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution. By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved. A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a heterogeneous medium.

Wave propagation improvement in two-dimensional bond-based peridynamics model

2021 ◽  
pp. 095440622098555
Author(s):  
Reza Alebrahim ◽  
Pawel Packo ◽  
Mirco Zaccariotto ◽  
Ugo Galvanetto
Keyword(s):  
Wave Propagation ◽  
Dynamic Performance ◽  
Numerical Dispersion ◽  
Motion Modeling ◽  
Minimization Method ◽  
Irregular Wave ◽  
Point Collocation ◽  
Potential Applications ◽  
Non Local ◽  
Set Up

In this study, methods to mitigate anomalous wave propagation in 2-D Bond-Based Peridynamics (PD) are presented. Similarly to what happens in classical non-local models, an irregular wave transmission phenomenon occurs at high frequencies. This feature of the dynamic performance of PD, limits its potential applications. A minimization method based on the weighted residual point collocation is introduced to substantially extend the frequency range of wave motion modeling. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion curves and minimizing the error in the frequency-wavenumber domain. A significant improvement in the wave propagation simulation using Bond-Based PD is observed.

scholarly journals Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method

2013 ◽  
Vol 13 (4) ◽  
pp. 985-1012 ◽  
Author(s):  
Guillaume Chiavassa ◽  
Bruno Lombard
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressional Wave ◽  
Interface Conditions ◽  
Immersed Interface Method ◽  
Fluid Medium ◽  
Strang Splitting

AbstractNumerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-posedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time- marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.

Study of internal stresses in rock massif within the framework of elastic layered block models with inclusions of the hierarchical structure of the L-rank.

2021 ◽  
Author(s):  
Olga Hachay ◽  
Andrey Khachay
Keyword(s):  
Hierarchical Structure ◽  
Classical Theory ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Heterogeneous Media ◽  
Theory Of Elasticity ◽  
Rock Massif ◽  
Local Theory ◽  
Internal Stresses ◽  
Non Local

<p>In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as in complex massifs in mine conditions. The paper presents an algorithm for the propagation of longitudinal acoustic waves in the framework of active well monitoring of elastic layered block media with inclusions of hierarchical type of L-th rank. Relations for internal stresses and strains for each hierarchical rank are obtained, which constitute the non local theory of elasticity. The essential differences between the non local theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a rock massif. Thanks to the use of a model of a layered block medium with hierarchical inclusions, it is possible, using borehole acoustic monitoring, to determine the position of the highest values ​​of internal stresses and, with less effort, to implement the method of unloading the rock massif. If it is necessary to conduct short-term predictive monitoring of geodynamic regions and determine a more accurate position of the source of a dynamic phenomenon using borehole active acoustic observations, it is necessary to use the values ​​of the tensor of internal hierarchical stresses as a monitored parameter.</p>

Wave Propagation in Heterogeneous Media. Part 1: Effective Velocities in Fractured Media

2002 ◽  
pp. 469-475
Author(s):  
Erik H. Saenger ◽  
Heiko Priller ◽  
Christian Grosse ◽  
Peter Hubral ◽  
Serge A. Shapiro
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Fractured Media
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