Smoothed Particle Hydrodynamics: Some recent improvements and applications

doi:10.1016/S0045-7825(96)01090-0

Computer Methods in Applied Mechanics and Engineering

Volume 139, Issues 1–4, 15 December 1996, Pages 375-408

https://doi.org/10.1016/S0045-7825(96)01090-0 Get rights and content

Abstract

The Smoothed Particle Hydrodynamics (SPH) computing technique has features which make it highly attractive for simulating dynamic response of materials involving fracture and fragmentation. However, full exploitation of the method's potential has been hampered by some unresolved problems including stability and the lack of generalized boundary conditions. We address these difficulties and propose solutions. Continuum damage modeling of fracture is discussed at length with scalar and tensor formulations proposed and tested within SPH. Several recent applications involving fracture with predicted fragment patterns and mass distributions are compared with experiment.

References (48)

L.D. Libersky et al.
High strain Lagrangian hydrodynamics
J. Comput. Phys.
(1993)
J.J. Monaghan et al.
Shock simulation by the particle method SPH
J. Comput. Phys.
(1983)
D.A. Flanagan et al.
An accurate numerical algorithm for stress integration with finite rotations
Comput. Methods Appl. Mech. Engrg.
(1987)
J.W. Swegle et al.
Smoothed particle hydrodynamics stability analysis
J. Comput. Phys.
(1995)
D.S. Balsara
von Neumann Stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms
J. Comput. Phys.
(1995)
C.T. Dyka et al.
An approach for tension instability in smoothed particle hydrodynamics
Comput. Struct.
(1995)
W. Benz et al.
Impact simulations with fracture. I. Methods and tests
ICARUS
(1994)
W. Benz et al.
Simulations of brittle solids using smoothed particle hydrodynamics
Comput. Phys. Comm.
(1995)
D.E. Grady et al.
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1980)
G.R. Johnson et al.
Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, and pressures
Engrg. Fract. Mech.
(1985)

P.W. Randles et al.

A continuum damage model for thick composite materials subjected to high-rate dynamic loading

Mech. Mater.

(1992)

J.A. Nemes et al.

Constitutive modeling of high strain-rate deformation and spall fracture of graphite/peek composites

Mech. Mater.

(1994)

A.J. Piekutowski

A simple dynamic model for the formation of debris clouds

Int. J. Impact Engrg.

(1990)

A.G. Petschek et al.

Cylindrical smoothed particle hydrodynamics

J. Comput. Phys.

(1993)

L.B. Lucy

A numerical approach to the testing of the fission hypothesis

Astron. J.

(1977)

R.A. Gingold et al.

Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars

Mon. Not. R. Astr. Soc.

(1977)

L.D. Libersky et al.

Smoothed particle hydrodynamics with strength of materials

Y. Wen et al.

Stabilizing SPH with Conservative Smoothing

Sandia Report, SAND94-1932

(1994)

G.R. Johnson and S.R. Beissel, Normalized smoothing functions for impact computations, Int. J. Numer. Methods Engrg.,...

D. Everhart, Private communication,...

W. Benz

G.V. Bicknell

SIAM J. Sci. Stat. Comput.

(1991)

W. Herrmann

Constitutive equations for large dynamic deformations

G.R. Johnson et al.

A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures

Cited by (1174)

An offline coupling approach for efficient SPH simulations of long-distance tsunami events using wave source boundary condition
2024, Advances in Engineering Software
The entire procedure of tsunami events consists of wave generation and propagation toward the coastal structures encompassing the long-range system domain. Therefore, instead of an integrated continuous simulation, two or several consecutive simulations are preferred for numerical efficiency, where the hydrodynamic information within a particular domain from the preceding simulation can be utilized for the wave sources in the subsequent simulation. In this study, as an offline coupling approach, the wave source boundary condition is proposed based on the particle-based Lagrangian framework. This boundary condition is integrated with the solution algorithm of the smoothed particle hydrodynamics (SPH) in-house parallel code. In the dambreak simulation, it is validated that the wave source boundary condition can encompass both the forward and reverse flows, where the numerical results of the full and partial simulations show good agreement in terms of the wave profile, velocity distributions, and measured pressure histories. Thereafter, the full and partial simulations of a tsunami experiment are carried out. The numerical results in the partial simulation agree well with those obtained in the full simulation in terms of the particle distributions, physical quantities, and loading histories (e.g., pressure, acceleration) on the shoreline structure. It is demonstrated that the proposed offline coupling approach using the wave source boundary condition is compatibly utilized with the developed in-house SPH parallel solver, facilitating the detailed FSI simulations within a reduced domain of interest for long-distance tsunami-like phenomena.
Comparative study of WCSPH, EISPH and explicit incompressible-compressible SPH (EICSPH) for multi-phase flow with high density difference
2024, Journal of Computational Physics
This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian–Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and reformulated in the ALE framework. The Explicit Incompressible-Compressible SPH (EICSPH) method, which can handle both compressible and incompressible phases, is developed by combining these two approaches in a fully explicit algorithm. The proposed methods are validated and compared through four benchmark problems including Rayleigh-Taylor instability, hydrostatic, liquid sloshing and dam break problems. Firstly, the stability and accuracy of interface modeling of the three methods were verified through Rayleigh-Taylor instability with small density differences. In the hydrostatic problem with a large density difference, the results from all three methods exhibit good agreement in the pressure distribution. Particularly, EICSPH demonstrates the faster convergence when compared to WCSPH, with EISPH showing fastest convergence overall. In the transient sloshing problem, all three methods quantitatively converged to the experimental results and exhibited good agreement, although slight pressure noise was observed in WCSPH initially. Finally, in the dam break problem, all three methods successfully simulated sharp interfaces without non-physical voids. The temporal variations of pressure and height were well predicted by all three methods, with EISPH showing better conformity to the water-air interface morphology obtained from other incompressible numerical methods compared to WCSPH and EICSPH. Additionally, the impact of air speed of sound was examined in EICSPH, where while the difference in pressure variation at the probe was minimal, differences were observed in energy dissipation and the progression of the free surface due to the air cushion effect.
A depth-averaged SPH-FV landslide dynamic model for evaluating hazard zones
2024, Computers and Geotechnics
Thousands of landslides worldwide lead to significant casualties and property damage. A numerical model is crucial for simulating the runout of possible future landslides and generating reliable hazard zone maps. Two main methods can be adopted to simulate motion: one based on the Eulerian description and the other based on the Lagrangian description. Each description offers varying adaptability to simulating landslides. In this paper, we proposed a method of coupling the depth-averaged smoothed particle hydrodynamics (SPH) method and a finite volume scheme with the van Leer splitting (FV-VLS). For the solid phase, we utilized the depth-averaged SPH method to simulate the movement process. The SPH method can track the movement of key parts. In contrast, we employed the FV-VLS based on the Eulerian description to reduce the calculation amount. In 1-D dam break simulation, both the depth-averaged SPH and FV-VLS methods yielded similar results. The 1-D two-phase dam break simulation shows that buoyancy reduces friction and lateral solid stress, increases hydraulic stress, and generates a complex motion process. The Yigong landslide simulation indicates that solid fractions will affect the motion trajectory in the 2-D simulation. A smaller solid fraction will cause the landslide to affect a larger area.
Adaptive moving window technique for SPH simulation of stationary shock waves
2024, Computer Physics Communications
A novel adaptive moving window (AMW) technique is developed for simulating stationary shock waves in a moving coordinate system associated with a simulation box. The velocity of this system is adjusted by an iterative feedback algorithm with the purpose of establishing a desirable position of shock front. Galilean transformations are iteratively used to maintain the shape of the flow profile. The moving coordinate system has advantages in simulation over a conventional coordinate system associated with the intact material at rest. In particular, a truly steady flow regime can be established in this moving window (MW). Comparative simulation using the smoothed particle hydrodynamics method to study shock propagation in copper confirms that the AMW converges to a steady state faster than a MW technique with a fixed velocity. We demonstrate that AMW can be applied for very weak shocks. Advantage of AMW is revealed in SPH simulation of the front structure for weak shocks in porous copper that result in a partial pore compaction. Specifically, we clarify the mechanism of the partial pore collapse for shock velocities below a knee on a calculated shock Hugoniot, where this knee corresponds to the complete collapse of pores.
SPH numerical simulation of SC-CO<inf>2</inf> directional fracturing and emulsion explosives for rock breaking
2024, Gas Science and Engineering
SC-CO₂ (Supercritical carbon dioxide) directional fracturing is a promising alternative to explosive blasting in complex environments. This study aims to establish an equivalent method for directional fracturing using traditional explosives, promoting broader adoption of this technology. We conduct a comparative experiment analyzing explosive and SC-CO₂ rock breaking, developing the SPH (Smoothed Particle Hydrodynamics) numerical model that includes characteristics of the rock-breaking area and dynamic effects of SC-CO₂ and explosives. Additionally, we investigate the influence of the directional fracturing device on the energy release coefficient. Proposing a numerical simulation method for SC-CO₂ directional fracturing based on equivalence to No.2 rock emulsion explosive, we use the SPH particle algorithm to enhance visualization of the rock-breaking area. Our findings show that the explosive method yields a larger rock-breaking volume than SC-CO₂. Under identical explosive charges, the directional cracker model inhibits explosive energy release, with energy decreasing as distance increases. Calculating an inhibition coefficient of 0.45 for the cracker model in terms of explosive granite, the rock-breaking volume index is 0.48, with an average value of 0.465. In mudstone sites, a similar trend is observed with an average energy release inhibition coefficient of 0.44.
A robust δ-SPH<sup>C</sup> model for nonlinear water wave interactions with structures under complex wave conditions
2024, Engineering Analysis with Boundary Elements
The problem of water wave interactions with marine structures, involving complex nonlinear characteristics such as large deformation of free-surface and violent structural motion, has been the focus and challenge of research in naval, coastal and ocean engineering. Recently, the $δ$ -SPH $^{C}$ model has been successfully applied in numerical wave flumes despite some minor flaws in energy conservation. In the present study, a robust $δ$ -SPH $^{C}$ with a better property regarding energy conservation is further formulated to simulate the hydrodynamic problems of various nonlinear water waves and structures. Three numerical benchmarks, i.e., the coupling motion between second-order Stokes waves, solitary waves, focused waves and structures are implemented to validate the accuracy and stability of the fluid–structure interaction (FSI) model, respectively. Based on the numerical results, the strengths and weaknesses between the $δ$ -SPH, original and improved $δ$ -SPH $^{C}$ models in simulating the FSI problems are discussed. It is demonstrated that the present scheme performs fairly well in modeling nonlinear water wave–structure interactions.

View all citing articles on Scopus

View full text

Smoothed Particle Hydrodynamics: Some recent improvements and applications

Abstract

J. Comput. Phys.

J. Comput. Phys.

Comput. Methods Appl. Mech. Engrg.

J. Comput. Phys.

J. Comput. Phys.

Comput. Struct.

ICARUS

Comput. Phys. Comm.

Int. J. Rock Mech. Min. Sci. Geomech. Abstr.

Engrg. Fract. Mech.

Mech. Mater.

Mech. Mater.

Int. J. Impact Engrg.

J. Comput. Phys.

A numerical approach to the testing of the fission hypothesis

Astron. J.

Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars

Mon. Not. R. Astr. Soc.

Smoothed particle hydrodynamics with strength of materials

Stabilizing SPH with Conservative Smoothing

Sandia Report, SAND94-1932

SIAM J. Sci. Stat. Comput.

Constitutive equations for large dynamic deformations

A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures