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In this paper a simple, robust, and general purpose approach to implement the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is proposed. This approach is well suited for implementation on CPUs and GPUs. The method is…

Numerical Analysis · Mathematics 2021-05-06 Abhinav Muta , Prabhu Ramachandran , Pawan Negi

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

In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which…

Mathematical Physics · Physics 2016-02-16 Joep H. M. Evers , Iason A. Zisis , Bas J. van der Linden , Manh Hong Duong

A new means of incorporating radiative transfer into smoothed particle hydrodynamics (SPH) is introduced, which builds on the success of two previous methods - the polytropic cooling approximation as devised by Stamatellos et al (2007), and…

Astrophysics · Physics 2009-11-13 Duncan Forgan , Ken Rice , Dimitris Stamatellos , Anthony Whitworth

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation…

Astrophysics · Physics 2009-11-13 D. Garcia-Senz , A. Relano , R. M. Cabezon , E. Bravo

In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative…

Astrophysics · Physics 2009-11-13 D. J. Price , J. J. Monaghan

Smoothed Particle Hydrodynamics (SPH) is a frequently applied tool in computational astrophysics to solve the fluid dynamics equations governing the systems under study. For some problems, for example when involving asteroids and asteroid…

Instrumentation and Methods for Astrophysics · Physics 2023-11-20 Irina Sagert , Oleg Korobkin , Ingo Tews , Bing-Jyun Tsao , Hyun Lim , Michael J. Falato , Julien Loiseau

A unified Smoothed Particle Hydrodynamics (SPH) framework is proposed to simulate interaction dynamics involving thin shells modeled by a reduced-dimensional, single-layer particle discretization, as opposed to full-dimensional SPH solids.…

Fluid Dynamics · Physics 2026-02-24 Dong Wu , Shuaihao Zhang , Weiyi Kong , Xiangyu Hu

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy,…

Instrumentation and Methods for Astrophysics · Physics 2016-08-08 Domingo García-Senz , Rubén M. Cabezón , José A. Escartín , Kevin Ebinger

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

We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…

General Relativity and Quantum Cosmology · Physics 2011-05-10 Juan P. Cruz , José A. González

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

This paper presents a divergence cleaning formulation for the velocity in the weakly compressible smoothed particle hydrodynamics (SPH) scheme. The proposed hyperbolic/parabolic divergence cleaning, ensures that the velocity divergence,…

Fluid Dynamics · Physics 2025-05-01 Georgios Fourtakas , Renato Vacondio , Benedict D. Rogers

Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of…

Fluid Dynamics · Physics 2016-02-23 Dede Tarwidi

To make relevant predictions about observable emission, hydrodynamical simulation codes must employ schemes that account for radiative losses, but the large dimensionality of accurate radiative transfer schemes is often prohibitive.…

Instrumentation and Methods for Astrophysics · Physics 2015-06-23 James C. Lombardi , William G. McInally , Joshua A. Faber

The problem of consistency of smoothed particle hydrodynamics (SPH) has demanded considerable attention in the past few years due to the ever increasing number of applications of the method in many areas of science and engineering. A loss…

Numerical Analysis · Mathematics 2016-05-18 Leonardo Di G. Sigalotti , Jaime Klapp , Otto Rendón , Carlos A. Vargas , Franklin Peña-Polo

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

Direct numerical simulation of subsonic turbulence with smoothed particle hydrodynamics (SPH) has traditionally been hampered by zeroth-order (E0) errors, inaccurate gradient evaluations, and excessive numerical dissipation. We demonstrate…

Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is…

Computational Engineering, Finance, and Science · Computer Science 2023-07-13 Kanishka Bhattacharya , Tapan Jana , Amit Shaw , L. S. Ramachandra , Vishal Mehera

We review the current status of compact object simulations that are based on the Smooth Particle Hydrodynamics (SPH) method. The first main part of this review is dedicated to SPH as a numerical method. We begin by discussing relevant…

Instrumentation and Methods for Astrophysics · Physics 2015-10-14 S. Rosswog
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