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The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that…

Instrumentation and Methods for Astrophysics · Physics 2009-11-09 Stephan Rosswog

A novel numerical formulation for solving fluid-structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element…

Computational Engineering, Finance, and Science · Computer Science 2021-06-16 Sebastian L. Fuchs , Christoph Meier , Wolfgang A. Wall , Christian J. Cyron

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-14 S. Hess , V. Springel

Smoothed Particle Hydrodynamics (SPH) is a ubiquitous numerical method for solving the fluid equations, and is prized for its conservation properties, natural adaptivity, and simplicity. We introduce the Sphenix SPH scheme, which was…

Astrophysics of Galaxies · Physics 2021-11-17 Josh Borrow , Matthieu Schaller , Richard G. Bower , Joop Schaye

The Smoothed Particle Hydrodynamics (SPH) is a particle-based, Lagrangian method for fluid-flow simulations. In this work, fundamental concepts of this method are first briefly recalled. Then, the ability to accurately model granular…

Geophysics · Physics 2016-02-26 Kamil Szewc

Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different…

Numerical Analysis · Mathematics 2017-12-01 Alexander A. Lukyanov , Kees Vuik

Particle methods play an important role in the study of a wide variety of astrophysical fluid dynamics problems. The different methods currently in use are all variants of the so-called Smoothed Particle Hydrodynamics (SPH) scheme…

Astrophysics · Physics 2009-10-31 Frederic A. Rasio

The numerical accuracy of particle-based approximations in Smoothed Particle Hydrodynamics (SPH) is significantly affected by the spatial uniformity of particle distributions, especially for second-order derivatives. This study aims to…

Numerical Analysis · Mathematics 2026-01-29 Zhonghua Qiao , Yifan Wei

Smoothed particle hydrodynamics (SPH) method has been increasingly used for simulating fluid flows, however its ability to simulate evaporating flow requires significant improvements. This paper proposes an SPH method for evaporating…

Computational Physics · Physics 2017-09-20 Xiufeng Yang , Song-Charng Kong

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving…

The solidification behavior of liquid metal in a container under rapid cooling process is one of the major concerns to be analyzed. In order to analyze its fundamental behavior, a three- dimensional (3D) fluid dynamics simulation was…

Fluid Dynamics · Physics 2013-09-18 Raden Ahnaf Faqih S , Christian Fredy Naa

Simulating the flow of different fluids can be a highly computational intensive process, which requires large amounts of resources. Recently there has been a lot of research effort directed towards GPU processing, which can greatly increase…

Computational Engineering, Finance, and Science · Computer Science 2019-07-17 Adrian Coman , Elena Apostol , Catalin Leordeanu , Emil Slusanschi

In fluid dynamical simulations in astrophysics, large deformations are common and surface tracking is sometimes necessary. Smoothed Particle Hydrodynamics (SPH) method has been used in many of such simulations. Recently, however, it has…

Instrumentation and Methods for Astrophysics · Physics 2017-03-29 Satoko Yamamoto , Junichiro Makino

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions…

Numerical Analysis · Mathematics 2007-12-02 R. A. Brownlee , P. Houston , J. Levesley , S. Rosswog

Various formulations of smooth-particle hydrodynamics (SPH) have been proposed, intended to resolve certain difficulties in the treatment of fluid mixing instabilities. Most have involved changes to the algorithm which either introduce…

Instrumentation and Methods for Astrophysics · Physics 2018-06-19 Philip F. Hopkins

Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…

Computational Engineering, Finance, and Science · Computer Science 2026-05-14 Mridul Tiwari , Sawan Kumar , Md Rushdie Ibne Islam , Souvik Chakraborty

The accuracy of meshless methods like Smoothed Particle Hydrodynamics (SPH) is highly dependent on the quality of the particle distribution. Existing particle initialization techniques often struggle to simultaneously achieve adaptive…

Computational Physics · Physics 2026-01-01 Navaneet Villodi , Prabhu Ramachandran

Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique developed for simulating complex fluid flows. Among its key ingredients is the use of nonlocal integral relaxations to local differentiations. Mathematical analysis of…

Numerical Analysis · Mathematics 2019-07-04 Qiang Du , Xiaochuan Tian

This study proposes a generalized coordinates based smoothed particle hydrodynamics (GSPH) method with overset methods using a Total Lagrangian (TL) formulation for large deformation and crack propagation problems. In the proposed GSPH, the…

Computational Engineering, Finance, and Science · Computer Science 2021-05-24 Huachao Deng , Yoshiaki Abe , Tomonaga Okabe

This paper proposes a novel consistent {\delta}+- Updated Lagrangian Particle Hydrodynamics (ULPH) model. Although the Smoothed Particle Hydrodynamics (SPH) model has gained recognized achievements, it is afflicted by excessive numerical…

Fluid Dynamics · Physics 2025-11-13 Shi-Xian Wu , Peng-Nan Sun , Xiao-Ting Huang , Yu-Xiang Peng , Andrea Colagrossi