Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

Chiavassa, Guillaume; Lombard, Bruno

doi:10.1016/j.jcp.2011.03.030

Cited by 36 publications

(55 citation statements)

References 48 publications

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“…We have no theoretical estimate of RðSÞ, but numerical studies have shown that this value is similar to that of the spectral radius in LF: ðg=jÞðq=vÞ, which can be very large. 6 The time step can therefore be highly penalized in this case [Eq. (40)].…”

Section: A Splittingmentioning

confidence: 99%

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A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability

Blanc

Chiavassa

Lombard

2013

The Journal of the Acoustical Society of America

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An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amount to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: The convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: The propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.

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Section: A Splittingmentioning

confidence: 99%

“…5 and the introduction to Ref. 6 for general reviews. In the HF regime, the fractional derivatives greatly complicate the numerical modeling of the Biot-JKD equations.…”

Section: Introductionmentioning

confidence: 99%

A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability

Blanc

Chiavassa

Lombard

2013

The Journal of the Acoustical Society of America

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“…Appendix B. Scattering of a plane wave at oblique incidence on a plane homogenized interface We consider a plane wave at oblique incidence θ on the thick interface and the problem to solve is (5). We want to determine u(x, y, ω) in (42), and u is defined in (7). Below, we shall calculate the pressure p afterwards u = (v x , v y , p) T is deduced using (5) written in the harmonic regime, with time dependence e −iωt , whence…”

Section: Resultsmentioning

confidence: 99%

“…Let us begin with the classical case of acoustics where the jump conditions do not involve spatial derivatives: for instance, v n = 0 and p = 0. In this case, taking k = r maintains a r-th order global accuracy [7] (the criterion k = r − 1 is even sufficient [8]). In the non-classical case studied here, the jump conditions involve first-order spatial derivatives.…”

Section: High-order Compatibility Condition Eq (12)mentioning

confidence: 99%

Numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain

Lombard

Maurel

Marigo

2017

Journal of Computational Physics

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Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt an immersed interface method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in an homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.

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“…The purpose of this paper is to simulate wave propagation for transverse porous media. For the LF-Biot equations, we use the direct method to handle the viscous term, which is different from the splitting method [16,26,13]; both the single material and heterogeneous materials with point source tests are considered. For the Biot-JKD equations, we applied the technique developed in [35] for dealing with the memory term and solve the augmented Biot-JKD equations, which deal with the memory terms by using auxiliary variables derived from the JKD-tortuosity.…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms

Xie

2019

Journal of Computational Physics

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In this paper, we investigate wave propagation in orthotropic poroelastic media by studying the timedomain poroelastic equations. Both the low frequency Biot's (LF-Biot) equations and the Biot-Johnson-Koplik-Dashen (Biot-JKD) models are considered. In LF-Biot equations, the dissipation terms are proportional to the relative velocity between the fluid and the solid by a constant. Contrast to this, the dissipation terms in the Biot-JKD model are in the form of time convolution (memory) as a result of the frequency-dependence of fluid-solid interaction at the underlying microscopic scale in the frequency domain. The dynamic tortuosity and permeability described by Darcy's law are two crucial factors in this problem, and highly linked to the viscous force. In the Biot model, the key difficulty is to handle the viscous term when the pore fluid is viscous flow. In the Biot-JKD dynamic permeability model, the convolution operator involves order 1/2 shifted fractional derivatives in the time domain, which is challenging to discretize.In this work, we utilize the multipoint Padé (or Rational) approximation for Stieltjes function to approximate the dynamic tortuosity and then obtain an augmented system of equations which avoids storing the solutions of the past time. The Runge-Kutta discontinuous Galerkin (RKDG) method is used to compute the numerical solution, and numerical examples are presented to demonstrate the high order accuracy and stability of the method.

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Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

Cited by 36 publications

References 48 publications

A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability

A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability

Numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain

A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms

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