An improved CSPM approximation for multi-dimensional second-order derivatives

Stan Korzilius; Wil H.A. Schilders; Martijn J.H. Anthonissen

An improved CSPM approximation for multi-dimensional second-order derivatives

Stan Korzilius, Wil H.A. Schilders, Martijn J.H. Anthonissen

Center for Analysis, Scientific Computing and Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Many SPH approximations for second-order derivatives, or the Laplacian, suffer
from the presence of boundaries and irregularities in the particle distribution.
In this papier we discuss four estimates to the Laplacian: the Brookshaw approximation, CSPM, MSPH and ICSPM – the latter of which is derived in
this work. We theoretically derive the convergence rate of these methods and
validate the results with numerical experiments. We show that the widely
used Brookshaw method suffers the most from boundaries or random particles,
while MSPH and the method derived in this work (ICSPM) are able to stay
accurate. ICSPM uses smaller matrices then MSPH and is therefore computationally more attractive.

Original language	English
Title of host publication	10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015)
Pages	39-44
Publication status	Published - 2015
Event	conference; 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop; 2015-06-16; 2015-06-18 - Parma, Italy Duration: 16 Jun 2015 → 18 Jun 2015

Conference

Conference	conference; 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop; 2015-06-16; 2015-06-18
Country/Territory	Italy
City	Parma
Period	16/06/15 → 18/06/15

Cite this

@inproceedings{0c74960a768c435f808495c72df9f895,

title = "An improved CSPM approximation for multi-dimensional second-order derivatives",

abstract = "Many SPH approximations for second-order derivatives, or the Laplacian, sufferfrom the presence of boundaries and irregularities in the particle distribution.In this papier we discuss four estimates to the Laplacian: the Brookshaw approximation, CSPM, MSPH and ICSPM – the latter of which is derived inthis work. We theoretically derive the convergence rate of these methods andvalidate the results with numerical experiments. We show that the widelyused Brookshaw method suffers the most from boundaries or random particles,while MSPH and the method derived in this work (ICSPM) are able to stayaccurate. ICSPM uses smaller matrices then MSPH and is therefore computationally more attractive.",

author = "Stan Korzilius and Schilders, {Wil H.A.} and Anthonissen, {Martijn J.H.}",

year = "2015",

language = "English",

pages = "39--44",

booktitle = "10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015)",

note = "null ; Conference date: 16-06-2015 Through 18-06-2015",

}

Korzilius, S , Schilders, WHA & Anthonissen, MJH 2015, An improved CSPM approximation for multi-dimensional second-order derivatives. in 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015). pp. 39-44, conference; 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop; 2015-06-16; 2015-06-18, Parma, Italy, 16/06/15.

An improved CSPM approximation for multi-dimensional second-order derivatives. / Korzilius, Stan ; Schilders, Wil H.A.; Anthonissen, Martijn J.H.

10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015). 2015. p. 39-44.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - An improved CSPM approximation for multi-dimensional second-order derivatives

AU - Korzilius, Stan

AU - Schilders, Wil H.A.

AU - Anthonissen, Martijn J.H.

PY - 2015

Y1 - 2015

N2 - Many SPH approximations for second-order derivatives, or the Laplacian, sufferfrom the presence of boundaries and irregularities in the particle distribution.In this papier we discuss four estimates to the Laplacian: the Brookshaw approximation, CSPM, MSPH and ICSPM – the latter of which is derived inthis work. We theoretically derive the convergence rate of these methods andvalidate the results with numerical experiments. We show that the widelyused Brookshaw method suffers the most from boundaries or random particles,while MSPH and the method derived in this work (ICSPM) are able to stayaccurate. ICSPM uses smaller matrices then MSPH and is therefore computationally more attractive.

AB - Many SPH approximations for second-order derivatives, or the Laplacian, sufferfrom the presence of boundaries and irregularities in the particle distribution.In this papier we discuss four estimates to the Laplacian: the Brookshaw approximation, CSPM, MSPH and ICSPM – the latter of which is derived inthis work. We theoretically derive the convergence rate of these methods andvalidate the results with numerical experiments. We show that the widelyused Brookshaw method suffers the most from boundaries or random particles,while MSPH and the method derived in this work (ICSPM) are able to stayaccurate. ICSPM uses smaller matrices then MSPH and is therefore computationally more attractive.

M3 - Conference contribution

SP - 39

EP - 44

BT - 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015)

Y2 - 16 June 2015 through 18 June 2015

ER -