Non-smooth kernels for meshfree methods in fluid dynamics

Authors:
J. -M. Belley;P. Belley;F. Colin;R. Egli
Affiliations:
Faculté des sciences, Université de Sherbrooke, Sherbrooke (QC), J1K2R1, Canada;Faculté des sciences, Université de Sherbrooke, Sherbrooke (QC), J1K2R1, Canada;Department of Mathematics and Computer Science, Laurentian University, Sudbury (ON), P3E 2C6, Canada;Faculté des sciences, Université de Sherbrooke, Sherbrooke (QC), J1K2R1, Canada
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton-Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are derived.