Chapter

Principles of the SPH method

D. Violeau

in Fluid Mechanics and the SPH Method

Published in print May 2012 | ISBN: 9780199655526
Published online September 2012 | e-ISBN: 9780191741227 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655526.003.0005
Principles of the SPH method

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SPH is presented here as a discrete interpolating method. Continuous (integral) and discrete interpolations are introduced and their accuracy studied. SPH renormalization is presented through the concepts of invariance. Lagrangian SPH operators are built and used to discretise the equations of fluid motion. The latter are then revisited from a Lagrangian point of view based on the least action principle, and the conservations laws are deduced, in connection with Chapters 1 and 3. Numerical considerations are finally given. In particular, the choice of a time integrator is studied from the Hamilton equations, leading to suitable conservation properties with a discretized time. Finally, the numerical stability properties of the various SPH schemes are studied in arbitrary dimension.

Keywords: SPH; interpolating kernel; particles; time integrator; numerical stability

Chapter.  47518 words.  Illustrated.

Subjects: Condensed Matter Physics

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