Some comparisons and analyses of time or space discontinuous Galerkin methods applied to elastic wave propagation in anisotropic and heterogeneous media

Tié, Bing

doi:10.1186/s40323-019-0127-x

Cited by 3 publications

(4 citation statements)

References 19 publications

(54 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…At last, an explicit two-step second-order Runge-Kutta time-discretization is used to derive the discrete system. The reader interested in more details about formulation, implementation and stability of DG methods for anisotropic and piecewise homogeneous media should refer to references [30,40,43].…”

Section: Discretizationmentioning

confidence: 99%

Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

Renaud¹,

Tié²,

Mouronval³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, the effect on the ultrasonic attenuation of the grain size heterogeneity in polycrystals is analyzed. First, new analytical developments allowing the extension of the unified theory of Stanke and Kino to general grain size distributions are presented. It is then shown that one can additively decompose the attenuation coefficient provided that groups of grains are defined. Second, the study is specialized to a bimodal distribution of the grain size for which microstructures are numerically modeled by means of the software Neper. The additive partition of the attenuation coefficient into contributions coming from large and small grains motivates the derivation of an optimization procedure for characterizing the grain size distribution. The aforementioned approach, which is based on a least squares minimization, is at last presented and illustrated on both analytical and numerical attenuation data. It is thus shown that the method provides satisfying approximations of volume fractions of large grains and modal equivalent diameters from the frequency-dependent attenuation coefficient.

show abstract

Section: Discretizationmentioning

confidence: 99%

Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

Renaud¹,

Tié²,

Mouronval³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…All the three fluxes defined in Theorem 3.2 are identical. They are all equal to the Käser's flux (30) and can be written as follows:…”

Section: Upwind Numerical Fluxes For the 1st-order Velocity-stress Symentioning

confidence: 99%

“…(36a) is straightforward. The symmetric form of the numerical flux (36b) can be obtained by remarking that, in the case of continuous material properties, the following equations hold (see Appendix A2): (30) should be worse than the 1st-order flux (31), as it does not use the perturbed…”

Section: Upwind Numerical Fluxes For the 1st-order Velocity-stress Symentioning

confidence: 99%

“…As an important remark, the analysis of stability of a space dG method is essential, because of the use of numerical fluxes. A stability analysis has been performed by the author for the velocity-stress wave formulation [30]. At the continuous level of the time and whatever the space dimension, the stability has been proved in the case of an isotropic or anisotropic elastic medium with continuous properties or an isotropic elastic medium with discontinuous properties.…”

Section: Polycrystalline Materialsmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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.

show abstract

A General Computational Formalism for Networks of Structured Grids

D'Ambrosio

Arcuri

D’Onghia

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Some comparisons and analyses of time or space discontinuous Galerkin methods applied to elastic wave propagation in anisotropic and heterogeneous media

Cited by 3 publications

References 19 publications

Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

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

A General Computational Formalism for Networks of Structured Grids

Contact Info

Product

Resources

About