Lattice Boltzmann method for multimode wave propagation in viscoelastic media and in elastic solids

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Abstract

This paper reports the lattice Boltzmann method (LBM) based formulation for viscoelastic fluids with both volumetric and shear viscoelasticity. The relaxation limit of the viscoelastic fluid formulation yields the LBM for elastic solids with both volumetric or pressure (p) and shear (s) wave propagation modes. The reflection of a two-dimensional p wave from an obstacle (wedge) inclined to the propagation direction of the p wave is studied together with the convergence and stability behavior of the LBM as the lattice size and lattice time step decrease. The model is capable of accurately predicting the mode change (p to s) due to the reflection. The model provides a unique unified approach capable of simulating fluids, viscoelastic fluids, and solids within a single LBM framework, thus avoiding interface problems between different simulation methods. The paper concentrates on the wave propagation part of the model, in the quasielastic regime.

Original languageEnglish (US)
Article number066703
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number6
DOIs
StatePublished - Jun 16 2011

Fingerprint

Lattice Boltzmann Method
Wave Propagation
Viscoelastic Fluid
wave propagation
fluids
Relaxation Limit
Interface Problems
Formulation
Viscoelasticity
Stability and Convergence
Inclined
Wedge
Simulation Methods
formulations
propagation modes
viscoelasticity
Model
Propagation
Fluid
Decrease

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

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abstract = "This paper reports the lattice Boltzmann method (LBM) based formulation for viscoelastic fluids with both volumetric and shear viscoelasticity. The relaxation limit of the viscoelastic fluid formulation yields the LBM for elastic solids with both volumetric or pressure (p) and shear (s) wave propagation modes. The reflection of a two-dimensional p wave from an obstacle (wedge) inclined to the propagation direction of the p wave is studied together with the convergence and stability behavior of the LBM as the lattice size and lattice time step decrease. The model is capable of accurately predicting the mode change (p to s) due to the reflection. The model provides a unique unified approach capable of simulating fluids, viscoelastic fluids, and solids within a single LBM framework, thus avoiding interface problems between different simulation methods. The paper concentrates on the wave propagation part of the model, in the quasielastic regime.",
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