An exact Riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling

Zhan, Qiwei; Ren, Qiang; Zhuang, Mingwei; Sun, Qingtao; Liu, Qing

doi:10.1016/j.cma.2017.09.007

Cited by 41 publications

(36 citation statements)

References 38 publications

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“…Figure C shows the detected signal profiles simulated by Wavenology EL. We validated the Wavenology EL result with that obtained by a discontinuous Galerkin pseudospectral time‐domain (DG‐PSTD) algorithm, which is a well‐established finite element software . The relative mean square (RMS) error between the two simulation systems is less than 2.9%, showing the high accuracy of Wavenology EL.…”

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 84%

“…To analyze the skull's impacts on the propagation of acoustic waves, we adapted a finite‐difference‐based (FD) commercial software Wavenology EL (Wave Computation Technologies, Inc., Durham, North Carolina) , which is capable of simulating acoustic wave propagation in complex structures. We calculated the acoustic pressure and velocity fields based on the following first‐order partial differential equation in a conservation form

\frac{\partial boldq}{\partial t} = ((), \frac{\partial boldf}{\partial x} + \frac{\partial boldg}{\partial y} + \frac{\partial boldh}{\partial z}) + boldb

where q is the quasi‐velocity‐strain, f , g and h represent the flux variables for three directions, and b is the space‐time‐dependent source vector. Specifically,

boldq = {(ρ v_{x}, ρ v_{y}, ρ v_{z}, ε_{xx}, ε_{yy}, ε_{zz}, 2 ε_{italicyz}, 2 ε_{italicxz}, 2 ε_{italicxy})}^{T}

boldf = {(τ_{italicxx}, τ_{italicyy}, τ_{italiczz}, v_{x}, 0, 0, 0, v_{z}, v_{y})}^{T}

boldg = {(τ_{xy}, τ_{yy}, τ_{yz}, 0, v_{y}, 0, v_{z}, 0, v_{x})}^{T}

boldh = (τ_{italicxz}, τ_{italicyz}, τ_{italiczz}, 0, 0, v_{z <...>})

…”

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 99%

“…At the beginning, the longitudinal spherical waves spread outward from the origin inside the skull cavity. Because of the acoustic impedance mismatch between the skull and water , reflection and refraction occur when the longitudinal waves reach the inner water‐skull boundary. The reflected waves continue to travel and oscillate inside the skull cavity.…”

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 99%

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Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Liang

Liu

Zhan

et al. 2019

Journal of Biophotonics

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Non‐invasive photoacoustic tomography (PAT) of mouse brains with intact skulls has been a challenge due to the skull's strong acoustic attenuation, aberration, and reverberation, especially in the high‐frequency range (>15 MHz). In this paper, we systematically investigated the impacts of the murine skull on the photoacoustic wave propagation and on the PAT image reconstruction. We studied the photoacoustic acoustic wave aberration due to the acoustic impedance mismatch at the skull boundaries and the mode conversion between the longitudinal wave and shear wave. The wave's reverberation within the skull was investigated for both longitudinal and shear modes. In the inverse process, we reconstructed the transcranial photoacoustic computed tomography (PACT) and photoacoustic microscopy (PAM) images of a point target enclosed by the mouse skull, showing the skull's different impacts on both modalities. Finally, we experimentally validated the simulations by imaging an in vitro mouse skull phantom using representative transcranial PAM and PACT systems. The experimental results agreed well with the simulations and confirmed the accuracy of our forward and inverse models. We expect that our results will provide better understanding of the impacts of the murine skull on transcranial photoacoustic brain imaging and pave the ways for future technical improvements.

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Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 84%

\frac{\partial boldq}{\partial t} = ((), \frac{\partial boldf}{\partial x} + \frac{\partial boldg}{\partial y} + \frac{\partial boldh}{\partial z}) + boldb

where q is the quasi‐velocity‐strain, f , g and h represent the flux variables for three directions, and b is the space‐time‐dependent source vector. Specifically,

boldq = {(ρ v_{x}, ρ v_{y}, ρ v_{z}, ε_{xx}, ε_{yy}, ε_{zz}, 2 ε_{italicyz}, 2 ε_{italicxz}, 2 ε_{italicxy})}^{T}

boldf = {(τ_{italicxx}, τ_{italicyy}, τ_{italiczz}, v_{x}, 0, 0, 0, v_{z}, v_{y})}^{T}

boldg = {(τ_{xy}, τ_{yy}, τ_{yz}, 0, v_{y}, 0, v_{z}, 0, v_{x})}^{T}

boldh = (τ_{italicxz}, τ_{italicyz}, τ_{italiczz}, 0, 0, v_{z <...>})

…”

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 99%

Section: Forward Model On a Digital Mouse Skullmentioning

confidence: 99%

See 1 more Smart Citation

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Liang

Liu

Zhan

et al. 2019

Journal of Biophotonics

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“…The space discontinuous Galerkin (dG) method is based on the use of spatially element-wise discontinuous finite element basis functions, and developing appropriate numerical fluxes on element interfaces is a key point for its success [1,2,3,4,5,6,7,8,9,10]. For this purpose, exact solving of the Riemann problem defined on element interfaces is usually recommended.…”

Section: Introductionmentioning

confidence: 99%

“…However, when it is applied to elastic media, upwind numerical fluxes solving exactly the Riemann problem can be easily done only in the case of continuous material properties due to the involvement of the fourth order elastic tensor. Recently, research work has been proposed for the derivation of numerical fluxes at physical interfaces, i.e., in the presence of material discontinuities, in 2D [7] or in 3D [6,9,10] cases.…”

Section: Introductionmentioning

confidence: 99%

Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces

Tié

Mouronval

2020

Computer Methods in Applied Mechanics and Engineering

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This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity-stress and velocity-strain wave formulations are considered. The proposed approach allows the derivation of upwind numerical fluxes in a well structured and hierarchical way according to the degree of inhomogeneity across a physical interface. The numerical fluxes that are exact solutions of a relevant Riemann problem defined at a physical interface are obtained. The developed explicit and intrinsic tensorial expressions of upwind numerical fluxes in multidimensional case allow a better understanding and analysis of the physical meaning of involved terms. As numerical applications, an example with a physical interface separating two materials, one anisotropic and the other isotropic, and an example of polycrystalline material that presents a particular case with a larger number of physical interfaces, are considered. The proposed numerical fluxes are numerically investigated and validated.

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Numerical simulation of polymer filling process by a combined finite element/discontinuous Galerkin/level set method

2018

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The filling process in injection molding involves polymer melt and air with large density/viscosity ratios and the transient free surface. It is treated as a challenging viscoelastic-Newtonian two-phase flow problem especially on irregular domains. In this paper, the complex filling process for the irregular cavity is simulated using a combined finite element/discontinuous Galerkin/level set method with application to the socket with five inserts, which is rarely investigated. The rheological behaviour of the viscoelastic fluid is predicted according to the eXtended Pom-Pom (XPP) constitutive model. The level set method proposed from prior literature is utilized to capture the moving interface because of its simplicity and efficiency. The hybrid continuous and discontinuous Galerkin method is utilized to solve the viscoelastic incompressible Navier-Stokes equations. The second order Runge Kutta discontinuous Galerkin (RKDG) method is employed to deal with the XPP constitutive equation and the level set equation due to their hyperbolic natures. This combined algorithm is convenient to cope with the irregular cavity and avoid any stabilization terms. We first investigate the filling process of the rectangular cavity without and with a diamond insert and compare with other numerical and experimental results to illustrate the validity of the coupled method. Moreover, the cavity of the socket with five inserts is considered an application case. We analyze the influences of the inlet velocity and elasticity on physical quantities such as stresses, stretch, etc. The simulation results could provide some numerical predictions for the polymer industry.

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An exact Riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling

Cited by 41 publications

References 38 publications

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Impacts of the murine skull on high‐frequency transcranial photoacoustic brain imaging

Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces

Numerical simulation of polymer filling process by a combined finite element/discontinuous Galerkin/level set method

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