A semi-analytical boundary integral method for radial functions with application to Smoothed Particle Hydrodynamics

Kostorz, Wawrzyniec; Esmail-Yakas, Anton

doi:10.1016/j.jcp.2020.109565

Cited by 3 publications

(32 citation statements)

References 9 publications

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“…Next, the model presented in this work was coupled with the semi‐analytical boundary integral method given in Reference 7. The radial function W used was the (polynomial) Wendland quintic C 2 kernel 14 and the one‐dimensional quadrature of choice was the ASR.…”

Section: Resultsmentioning

confidence: 99%

“…The problem situation is presented in Figure 1, where the support of a fluid–particle may be overlapping with both solid particles and the solid boundaries, leading to an incomplete support

Ω

for the kernel function. Since the discussion for the fixed boundary treatment has been handled in a previous work, 7 only the effect of the solid particles is discussed here.…”

Section: Methodsmentioning

confidence: 99%

“…The two‐dimensional version of the problem can be tackled in a similar fashion, with the assumption

β \geq 1

still in place and the derivation for

β < 1

being analogous. In this case the identity previously given in 7 can be applied

\begin{align} \int_{normalΩ \cap {normalΩ}^{'}} W & = \int_{\partial false(normalΩ \cap {normalΩ}^{'} false)} G_{W}^{false(2 false)} false(ρ false) {\overset{boldx}{true}}^{T} boldP false(boldx prefix- {boldx}_{a} false) d t \\ G_{W}^{false(2 false)} false(ρ false) & = \int_{0}^{1} ŝ W false(ρ ŝ false) d \overset{s,}{true} \end{align}

where t is an arbitrary parameterization of the boundary. We reorient the system so that the line connecting the centers of the solid and SPH particles is aligned with the x coordinate axis.…”

Section: Methodsmentioning

confidence: 99%

“…The two-dimensional version of the problem can be tackled in a similar fashion, with the assumption ≥ 1 still in place and the derivation for < 1 being analogous. In this case the identity previously given in 7 can be applied…”

Section: Two Dimensionsmentioning

confidence: 99%

“…In particular, works of Mayrhofer et al 5 and Chiron 6 present approaches for piecewise planar boundaries in three dimensions (3D). Our recent work 7 also addresses this issue and gives a simpler, more compact, and yet fully general method relying on one‐dimensional numerical integration only.…”

Section: Introductionmentioning

confidence: 99%

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Semi‐analytical treatment of spherical solids in smoothed‐particle hydrodynamics fluid simulations

Kostorz

Esmail-Yakas

2020

Numerical Meth Engineering

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A method for modeling mobile spherical solids in Smoothed Particle Hydrodynamics simulations utilizing the semi-analytical boundary formulation is given. The technique relies on evaluating individual contributions from ideally spherical bodies to the normalization factor and its gradient. A derivation is provided in both two and three dimensions (3D) and a close-form solution is given for an arbitrary polynomial kernel function in 3D. The method is validated and implemented in an Smoothed-Particle Hydrodynamics-Discrete Element Method code to evaluate the solid fraction and results are compared to the previous standard.

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Section: Resultsmentioning

confidence: 99%

“…The problem situation is presented in Figure 1, where the support of a fluid–particle may be overlapping with both solid particles and the solid boundaries, leading to an incomplete support

Ω

for the kernel function. Since the discussion for the fixed boundary treatment has been handled in a previous work, 7 only the effect of the solid particles is discussed here.…”

Section: Methodsmentioning

confidence: 99%

“…The two‐dimensional version of the problem can be tackled in a similar fashion, with the assumption

β \geq 1

still in place and the derivation for

β < 1

being analogous. In this case the identity previously given in 7 can be applied

\begin{align} \int_{normalΩ \cap {normalΩ}^{'}} W & = \int_{\partial false(normalΩ \cap {normalΩ}^{'} false)} G_{W}^{false(2 false)} false(ρ false) {\overset{boldx}{true}}^{T} boldP false(boldx prefix- {boldx}_{a} false) d t \\ G_{W}^{false(2 false)} false(ρ false) & = \int_{0}^{1} ŝ W false(ρ ŝ false) d \overset{s,}{true} \end{align}

where t is an arbitrary parameterization of the boundary. We reorient the system so that the line connecting the centers of the solid and SPH particles is aligned with the x coordinate axis.…”

Section: Methodsmentioning

confidence: 99%

Section: Two Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Semi‐analytical treatment of spherical solids in smoothed‐particle hydrodynamics fluid simulations

Kostorz

Esmail-Yakas

2020

Numerical Meth Engineering

Self Cite

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Semi‐analytical smoothed‐particle hydrodynamics correction factors for polynomial kernels and piecewise‐planar boundaries

Kostorz

Esmail-Yakas

2021

Numerical Meth Engineering

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This work presents a method of exactly and efficiently evaluating integrals of compactly supported (and otherwise) polynomial radial kernels near piecewise-planar boundaries. The technique is motivated by and has an immediate application in the smoothed-particle hydrodynamics method employing the semi-analytical boundary formulation. The current implementation is exact and fully general, avoiding any need for symbolic or numerical integration which previous implementations rely on. A detailed derivation and three compact implementations are provided and the latter can be easily modified to fit new and existing simulation codes. Applications and good performance are demonstrated on a number of test problems, where the semi-analytical boundary method can simulate complex boundaries using roughly half the boundary particles required in a ghost particle boundary method.

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A new SPH density formulation for 3D free-surface flows

Geara¹,

Martin²,

Adami³

et al. 2022

Computers & Fluids

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A semi-analytical boundary integral method for radial functions with application to Smoothed Particle Hydrodynamics

Cited by 3 publications

References 9 publications

Semi‐analytical treatment of spherical solids in smoothed‐particle hydrodynamics fluid simulations

Semi‐analytical treatment of spherical solids in smoothed‐particle hydrodynamics fluid simulations

Semi‐analytical smoothed‐particle hydrodynamics correction factors for polynomial kernels and piecewise‐planar boundaries

A new SPH density formulation for 3D free-surface flows

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