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

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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 languageEnglish
Title of host publication10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Parma, Italy, June 16-18, 2015)
Pages39-44
Publication statusPublished - 2015
Eventconference; 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop; 2015-06-16; 2015-06-18 - Parma, Italy
Duration: 16 Jun 201518 Jun 2015

Conference

Conferenceconference; 10th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop; 2015-06-16; 2015-06-18
CountryItaly
CityParma
Period16/06/1518/06/15

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