TY - GEN

T1 - Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution

AU - Stoyanovskaya, Olga

AU - Lisitsa, Vadim

AU - Anoshin, Sergey

AU - Markelova, Tamara

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Convergence analysis

KW - Numerical dispersion

KW - Smoothed particles hydrodynamics (SPH)

UR - http://www.scopus.com/inward/record.url?scp=85135029590&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9b84c221-9f1f-31b7-b0b8-4c694f0037f7/

U2 - 10.1007/978-3-031-10522-7_14

DO - 10.1007/978-3-031-10522-7_14

M3 - Conference contribution

AN - SCOPUS:85135029590

SN - 9783031105210

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 184

EP - 197

BT - Computational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings

A2 - Gervasi, Osvaldo

A2 - Murgante, Beniamino

A2 - Hendrix, Eligius M.

A2 - Taniar, David

A2 - Apduhan, Bernady O.

PB - Springer Science and Business Media Deutschland GmbH

T2 - 22nd International Conference on Computational Science and Its Applications, ICCSA 2022

Y2 - 4 July 2022 through 7 July 2022

ER -