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A compatibly differenced total energy conserving form of SPH
Author(s) -
Michael Owen J.
Publication year - 2014
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3912
Subject(s) - discretization , rotation formalisms in three dimensions , formalism (music) , mathematics , smoothed particle hydrodynamics , kinetic energy , mathematical optimization , classical mechanics , physics , statistical physics , mechanics , mathematical analysis , geometry , art , musical , visual arts
SUMMARY We describe a modified form of smoothed particle hydrodynamics (SPH) in which the specific thermal energy equation is based on a compatibly differenced formalism, guaranteeing exact conservation of the total energy. We compare the errors and convergence rates of the standard and compatible SPH formalisms on a variety of shock test problems with analytic answers. We find that the new compatible formalism reliably achieves the expected first‐order convergence for these analytic shock tests and, in all cases, improves the accuracy of the numerical solution over the standard formalism. We also examine the performance of our new formalism on a more complicated applied problem: the diversion of an asteroid by a kinetic impactor. We find the compatible discretization demonstrates measurable improvement in the convergence of properties such as the deflection velocity in this kind of applied problem as well. Copyright © 2014 John Wiley & Sons, Ltd.