Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution Full article
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22nd International Conference 04-07 Jul 2022 , Malaga |
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| Source | COMPUTATIONAL SCIENCE AND ITS APPLICATIONS – ICCSA 2022 Compilation, Springer Cham. 2022. 675 c. ISBN 978-3-031-10522-7. РИНЦ |
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| Output data | Year: 2022, Pages: 184-197 Pages count : 14 DOI: 10.1007/978-3-031-10522-7_14 | ||||||
| Tags | Convergence analysis; Numerical dispersion; Smoothed particles hydrodynamics (SPH) | ||||||
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Abstract:
The Smoothed Particle Hydrodynamics (SPH) method is a meshless Lagrangian method widely used in continuum mechanics simulation. Despite its wide application, theoretical issues of SPH approximation, stability, and convergence are among the unsolved problems of computational mathematics. In this paper, we present the application of dispersion analysis to the SPH approximation of one-dimensional gas dynamics equations to study numerical phenomena that appeared in practice. We confirmed that SPH converges only if the number of particles per wavelength increases while smoothing length decreases. At the same time, reduction of the smoothing length when keeping the number of particles in the kernel fixed (typical convergence results for finite differences and finite elements) does not guarantee the convergence of the numerical solution to the analytical one. We indicate the particular regimes with pronounced irreducible numerical dispersion. For coarse resolution, our theoretical findings are confirmed in simulations.
Cite:
Stoyanovskaya O.
, Lisitsa V.
, Anoshin S.
, Markelova T.
Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution
In compilation COMPUTATIONAL SCIENCE AND ITS APPLICATIONS – ICCSA 2022. – Springer Cham., 2022. – Т.13375, Part I. – C.184-197. – ISBN 978-3-031-10522-7. DOI: 10.1007/978-3-031-10522-7_14 Scopus OpenAlex
Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution
In compilation COMPUTATIONAL SCIENCE AND ITS APPLICATIONS – ICCSA 2022. – Springer Cham., 2022. – Т.13375, Part I. – C.184-197. – ISBN 978-3-031-10522-7. DOI: 10.1007/978-3-031-10522-7_14 Scopus OpenAlex
Dates:
| Published online: | Jul 15, 2022 |
Identifiers:
| Scopus: | 2-s2.0-85135029590 |
| OpenAlex: | W4285414554 |