Spectral properties of the SPH Laplacian operator

In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed. In the case of periodic Cartesian particle network, the eigenfunctions and eigenvalues of the SPH Laplacian are found on theoretical groun...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 75; no. 10; pp. 3649 - 3662
Main Authors Violeau, Damien, Leroy, Agnès, Joly, Antoine, Hérault, Alexis
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 15.05.2018
Elsevier BV
Elsevier
Subjects
Computational fluid dynamics
Conditioning
Discrete element method
Eigenvalues
Eigenvectors
Fluid flow
Fluid mechanics
Laplace transforms
Laplacian
Mechanics
Numerical analysis
Periodic variations
Physics
Smooth particle hydrodynamics
Spectrum
Spectrum analysis
SPH
Eigenvalues
SPH
Conditioning
Laplacian
Spectrum
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Summary:In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed. In the case of periodic Cartesian particle network, the eigenfunctions and eigenvalues of the SPH Laplacian are found on theoretical grounds. The theory agrees well with numerical eigenvalues. The effects of particle disorder and non-periodicity conditions are then investigated from numerical viewpoint. It is found that the matrix condition number is proportional to the square of the particle number per unit length, irrespective of the space dimension and kernel choice.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.02.023