A Numerical Experiment of Consecutive Reactions in a Bubble Column

Shimada, Naoki; Saiki, Rina; Tomiyama, Akio

doi:10.1252/kakoronbunshu.35.339

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…Although PMLs in a mathematical model described by partial differential equations are perfect matching mediums, PMLs in the numerical analyses are not; discretization of a PML changes phase velocities of propagating waves and generates reflection waves from the PML region. 13) Approximation of an infinite PML with finite thickness also generates reflection waves from the PML terminal. 1,14) Estimating matching performance and optimizing parameters of PMLs in a numerical domain are required before solving problems.…”

Section: Discussionmentioning

confidence: 99%

Perfectly Matched Layers in the Cylindrical and Spherical Coordinates for Elastic Waves in Solids

Shimada

Hasegawa

2010

Jpn. J. Appl. Phys.

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The material constants of perfectly matched layers (PMLs) in the cylindrical and spherical coordinates in the frequency domain are presented. Using the coordinate transformation laws of tensors on manifolds, the quotient rule, and complex coordinate stretching, we obtain the material parameters of PMLs in the real coordinate. Our results show that PML parameters for elastic waves may be determined by the same procedure in the Cartesian coordinates. However, this rule has been determined for PML material constants derived from the analytic continuation in the cylindrical and spherical coordinates by Zheng and Huang in 2002. Our derivation based on differential forms shows that this rule holds for PML parameters in any orthogonal coordinate system. #

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Section: Discussionmentioning

confidence: 99%

Perfectly Matched Layers in the Cylindrical and Spherical Coordinates for Elastic Waves in Solids

Shimada

Hasegawa

2010

Jpn. J. Appl. Phys.

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“…In numerical models, however, discretizing PMLs changes phase velocities of propagating waves and generates reflection waves from the PML region. 16) Furthermore, the approximation of infinite regions with finite thick layers also generates reflection waves from the PML terminal. 1,16,17) Estimating the matching performance and optimizing the parameters of PMLs in a numerical domain are required before solving problems.…”

Section: Introductionmentioning

confidence: 99%

“…16) Furthermore, the approximation of infinite regions with finite thick layers also generates reflection waves from the PML terminal. 1,16,17) Estimating the matching performance and optimizing the parameters of PMLs in a numerical domain are required before solving problems. Chew and Jin investigated the dependence of PML performance on attenuation parameters of the FE analysis of electromagnetic wave problems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

Shimada¹,

Hasegawa²,

Sato

2011

Jpn. J. Appl. Phys.

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A perfectly matched layer (PML) is useful for truncating the computation region of scattering problems in a finite element analysis (FEA). The approximation of the open region with thick layer and discretization of it with finite elements generates reflection waves from PML boundary. However, reflection powers generated by finite element discretization have not been quantified for elastic waves. In this paper, we explain the reflection from PMLs by discretized wave number analysis of elastic plane-wave scattering, and demonstrate that the results of discretized wave number analysis give satisfactory approximations of FEA.

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A Numerical Experiment of Consecutive Reactions in a Bubble Column

Cited by 2 publications

References 6 publications

Perfectly Matched Layers in the Cylindrical and Spherical Coordinates for Elastic Waves in Solids

Perfectly Matched Layers in the Cylindrical and Spherical Coordinates for Elastic Waves in Solids

Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

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