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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

Simulations using the Smoothed Particle Hydrodynamics (SPH) technique typically include numerical viscosity to model shocks and maintain particle order on the kernel scale. This numerical viscosity is composed of linear and quadratic terms,…

Solar and Stellar Astrophysics · Physics 2025-06-02 Cheng Chen , C. J. Nixon

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

We summarize the ideas that led to the Adaptive Smoothed Particle Hydrodynamics (ASPH) algorithm, with anisotropic smoothing and shock-tracking. We then identify a serious new problem for SPH simulations with shocks and radiative cooling…

Astrophysics · Physics 2007-05-23 Hugo Martel , Paul R. Shapiro

I discuss the key features of Smoothed Particle Hydrodynamics (SPH) as a numerical method - in particular the key differences between SPH and more standard grid based approaches - that are important to the practitioner. These include the…

Instrumentation and Methods for Astrophysics · Physics 2011-11-08 Daniel J. Price

Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of non-hydrodynamical nature. Under this approach, SPH…

Astrophysics · Physics 2009-10-22 Pablo Laguna

This paper presents a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method for solving the two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The turbulent wall-bounded flow with or without mild flow separation, a…

Fluid Dynamics · Physics 2025-01-31 Feng Wang , Zhongguo Sun , Xiangyu Hu

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

This paper develops an arbitrary-positioned buffer for the smoothed particle hydrodynamics (SPH) method, whose generality and high efficiency are achieved through two techniques. First, with the local coordinate system established at each…

Computational Engineering, Finance, and Science · Computer Science 2024-06-25 Shuoguo Zhang , Yu Fan , Yaru Ren , Bin Qian , Xiangyu Hu

The standard smoothed particle hydrodynamics (SPH) method suffers from tensile instability, resulting in particle clumping and void regions under negative pressure conditions. In this study, we extend the transport-velocity formulation of…

Fluid Dynamics · Physics 2024-11-22 Zhentong Wang , Oskar J. Haidn , Xiangyu Hu

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

Particle shifting techniques (PST) have been used to improve the accuracy of the Smoothed Particle Hydrodynamics (SPH) method. Shifting ensures that the particles are distributed homogeneously in space. This may be performed by moving the…

Fluid Dynamics · Physics 2022-03-15 Dinesh Adepu , Prabhu Ramachandran

In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…

Fluid Dynamics · Physics 2010-06-22 G. Lanzafame

In this study we investigated the capabilities of the mesh-free, Lagrangian particle method (Smoothed Particle Hydrodynamics, SPH) to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within…

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme using the Geometric Density average force expression (GDSPH). GDSPH has recently been shown to reduce the leading order errors and…

Instrumentation and Methods for Astrophysics · Physics 2020-07-31 Robert Wissing , Sijing Shen

A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH…

Fluid Dynamics · Physics 2018-02-13 X. Y. Hu , N. A. Adams

The Smoothed Particles Hydrodynamics (SPH) is a particle-based, meshfree, Lagrangian method used to simulate multidimensional fluids with arbitrary geometries, most commonly employed in astrophysics, cosmology, and computational…

Computational Engineering, Finance, and Science · Computer Science 2022-12-21 Aurélien Cavelan , Rubén M. Cabezón , Michal Grabarczyk , Florina M. Ciorba

The methods in the Gasoline2 Smoothed Particle Hydrodynamics (SPH) code are described and tested. Gasoline2 is the most recent version of the Gasoline code for parallel hydrodynamics and gravity with identical hydrodynamics to the Changa…

Instrumentation and Methods for Astrophysics · Physics 2018-06-13 James W. Wadsley , Benjamin W. Keller , Thomas R. Quinn

Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…

Instrumentation and Methods for Astrophysics · Physics 2015-12-15 Philip F. Hopkins , Matthias J. Raives

We present a consistent high-order staggered Lagrangian hydrodynamics framework designed to reconcile an underlying disparity in existing curvilinear formulations: the mismatch between quadrature-based "strong" mass conservation and the…

Numerical Analysis · Mathematics 2026-04-01 Zhiyuan Sun , Jun Liu , Pei Wang