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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…

This paper proposes a novel numerical method based on Godunov Smoothed Particle Hydrodynamics for special relativistic fluid dynamics. Our method utilizes a Riemann solver to describe shock, enhancing accuracy in strong shock waves. The…

Computational Physics · Physics 2025-10-22 Kanta Kitajima , Shu-ichiro Inutsuka , Izumi Seno

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

Standard formulations of smoothed particle hydrodynamics (SPH) are unable to resolve mixing at fluid boundaries. We use an error and stability analysis of the generalised SPH equations of motion to prove that this is due to two distinct…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-13 J. I. Read , T. Hayfield , O. Agertz

We present a set of new smoothing kernels for smoothed particle hydrodynamics (SPH) that improve the convergence of the method without any additional computational cost. These kernels are generated through a linear combination of other SPH…

Instrumentation and Methods for Astrophysics · Physics 2026-02-04 Robert Wissing , Thomas R. Quinn , Ben Keller , James Wadsley , Sijing Shen

The method of Smoothed Particle Hydrodynamics (SPH) has been widely studied and implemented for a large variety of problems, ranging from astrophysics to fluid dynamics and elasticity problems in solids. However, the method is known to have…

Instrumentation and Methods for Astrophysics · Physics 2013-10-16 Ruslan F. Gabbasov , Jaime Klapp-Escribano , Joel Suarez-Cansino , Leonardo Di G. Sigalotti

We compare the results for a set of hydrodynamical tests performed with the AMR finite volume code, MG and the SPH code, SEREN. The test suite includes shock tube tests, with and without cooling, the non-linear thin-shell instability and…

Instrumentation and Methods for Astrophysics · Physics 2015-06-15 D. A. Hubber , S. A. E. G. Falle , S. P. Goodwin

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

We present the results from a two-day study in which we discussed various implementations of Smooth Particle Hydrodynamics (SPH), one of the leading methods used across a variety of areas of large-scale astrophysical simulations. In…

Astrophysics · Physics 2007-05-23 Piet Hut , Lars Hernquist , George Lake , Jun Makino , Steve McMillan , Thomas Sterling

We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using…

Computational Physics · Physics 2024-08-22 Nicholas Frontiere , Cody D. Raskin , J. Michael Owen

We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast…

Instrumentation and Methods for Astrophysics · Physics 2024-02-20 Takuhiro Yuasa , Masao Mori

We test and improve the numerical schemes in our smoothed particle hydrodynamics (SPH) code for cosmological simulations, including the pressure-entropy formulation (PESPH), a time-dependent artificial viscosity, a refined timestep…

Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will…

Graphics · Computer Science 2020-01-29 Xiaowei He , Huamin Wang , Guoping Wang , Hongan Wang , Enhua Wu

The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number…

Instrumentation and Methods for Astrophysics · Physics 2015-06-04 Walter Dehnen , Hossam Aly

Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection. The conservation equations of mass, momentum and energy of fluid are…

Fluid Dynamics · Physics 2019-04-16 Xiufeng Yang , Song-Charng Kong

Smoothed particle hydrodynamics (SPH) is typically used for barotropic fluids, where the pressure depends only on the local mass density. Here, we show how to incorporate the entropy into the SPH, so that the pressure can also depend on the…

Fluid Dynamics · Physics 2024-06-21 Michal Pavelka , Vaclav Klika , Ondrej Kincl

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for…

Particle-based fluid simulations have emerged as a powerful tool for solving the Navier-Stokes equations, especially in cases that include intricate physics and free surfaces. The recent addition of machine learning methods to the toolbox…

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

We have carried out a hydrodynamical code comparison study of interacting multiphase fluids. The two commonly used techniques of grid and smoothed particle hydrodynamics (SPH) show striking differences in their ability to model processes…