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

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииComputational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings
РедакторыOsvaldo Gervasi, Beniamino Murgante, Eligius M. Hendrix, David Taniar, Bernady O. Apduhan
ИздательSpringer Science and Business Media Deutschland GmbH
Страницы184-197
Число страниц14
ISBN (печатное издание)9783031105210
DOI
СостояниеОпубликовано - 2022
Событие22nd International Conference on Computational Science and Its Applications, ICCSA 2022 - Malaga, Испания
Продолжительность: 4 июл 20227 июл 2022

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том13375 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция22nd International Conference on Computational Science and Its Applications, ICCSA 2022
СтранаИспания
ГородMalaga
Период04.07.202207.07.2022

Предметные области OECD FOS+WOS

  • 1.02 КОМПЬЮТЕРНЫЕ И ИНФОРМАЦИОННЫЕ НАУКИ
  • 1.01 МАТЕМАТИКА

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