Convergence of the Smoothed Particle Hydrodynamics Method for a Specific Barotropic Fluid Flow: Constructive Kernel Theory
Abstract
Smoothed particle hydrodynamics (SPH) is a popular particle- and kernel-based method for numerically computing solutions to fluid-flow problems. In this paper, we study the convergence of SPH for the Euler equations of a specific barotropic fluid. In contrast to previous works, we distinguish carefully between the smoothing and the discretization parameters and give explicit relations between both of them to guarantee convergence. This convergence heavily depends on certain properties of the underlying kernel. Hence, a large part of this paper is devoted to constructing compactly supported, radial kernels which possess the required properties.
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4752 - 4784
DOI: 10.1137/17M1157696
ISSN (online): 1095-7154
Copyright
© 2018, Society for Industrial and Applied Mathematics.
History
Submitted: 20 November 2017
Accepted: 20 June 2018
Published online: 6 September 2018
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Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : WE 2333/9-1
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