The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

Sigalotti, Leonardo Di G.; Klapp, Jaime; Gesteira, Moncho Gómez

doi:10.3389/fams.2021.797455

Cited by 18 publications

(14 citation statements)

References 57 publications

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“…• In most mass-particle meshfree methods, each particle carries a mass and a density. This results in the obvious notion of volume as V i = mi ρi , for mass m and density ρ [34,53]. During the initial particle generation process, masses are distributed to particles in a manner so as to make this method consistent.…”

Section: Volume Definitionmentioning

confidence: 99%

Volume and Mass Conservation in Lagrangian Meshfree Methods

Suchde¹,

Leithäuser²,

Kuhnert³

et al. 2023

Preprint

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Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

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Section: Volume Definitionmentioning

confidence: 99%

Volume and Mass Conservation in Lagrangian Meshfree Methods

Suchde¹,

Leithäuser²,

Kuhnert³

et al. 2023

Preprint

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“…27,28 Despite this, SPH has suffers several drawbacks in comparison with classical FEM. 29,30 In the present study, the particle inconsistency and tensile instability problems are solved by using the kerneral correction though Symmetric Smoothed Particle Hydrodynamics (SSPH) 31,32 and Total Lagrangian formulation in the initial undeformed configuration. 33,34 In the SSPH method defined by Batra and Zhang, 31 the formulation begins by the classical Taylor series expansion of a function u(x)…”

Section: Ssph Formulationmentioning

confidence: 99%

Symmetric SPH modeling of functionally graded nanocomposite plates subjected to low‐velocity impact

Li,

Lin,

Naceur

et al. 2023

Polymer Composites

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Functionally graded (FG) composites reinforced by carbon nanotubes (CNTs) have received extensive attention due to their excellent mechanical properties. The impact responses of FG‐CNT nanocomposites are analyzed by the developed meshless method. The temperature‐dependent material properties are expressed by way of the extended rule of mixture. The kinematics of the composite plate is established on the basis of the first‐order shear deformation theory. The modified Hertzian contact law is adopted to evaluate the impact loading between the plate and the impactor. The dynamic balance equations of the plate are constructed and computed by the Systemic Smoothed Particle Hydrodynamics (SSPH) method with strengthened prediction ability. The impacting behaviors of the FG‐CNT nanocomposite plate, as well as the parametric effects, are analyzed by the developed model and the suitability is clearly demonstrated.Highlights Impact of FG‐CNTRC is firstly solved by a self‐developed meshless SPH model. Strong capacity of the SPH impact model is clearly demonstrated. More CNTs close to the strike face would improve the impact resistance.

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“…Therefore, they maintain quasi-ordered particle distributions even in highly dynamical test problems. Second, approximate volume partitioning is achieved using a large number of neighbors 37 , 38 . Third, non-reflecting outlet boundary conditions are implemented by allowing the particles that leave the Venturi diffuser and enter the outflow zone to move according to an outgoing wave equation for the velocity field.…”

Section: Introductionmentioning

confidence: 99%

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

Sigalotti,

Alvarado-Rodríguez,

Aragón

et al. 2023

Sci Rep

Self Cite

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The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C$$^{2}$$ 2 Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests.

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The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

Cited by 18 publications

References 57 publications

Volume and Mass Conservation in Lagrangian Meshfree Methods

Volume and Mass Conservation in Lagrangian Meshfree Methods

Symmetric SPH modeling of functionally graded nanocomposite plates subjected to low‐velocity impact

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

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