Solving 2D Poisson-type equations using meshless SPH method

Shuai Liu; Jiao Li; Liang Chen; Yanjin Guan; Cunsheng Zhang; Fuzheng Gao; Jun Lin

Results in Physics (Jun 2019)

Solving 2D Poisson-type equations using meshless SPH method

Shuai Liu,
Jiao Li,
Liang Chen,
Yanjin Guan,
Cunsheng Zhang,
Fuzheng Gao,
Jun Lin

Affiliations

Shuai Liu: Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
Jiao Li: Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
Liang Chen: Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
Yanjin Guan: Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China; Suzhou Institute of Shandong University, Suzhou 215123, China
Cunsheng Zhang: Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
Fuzheng Gao: School of Mathematics, Shandong University, Jinan 250061, China
Jun Lin: Suzhou Institute of Shandong University, Suzhou 215123, China; Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China; Corresponding author at: Suzhou Institute of Shandong University, Suzhou 215123, China.

Journal volume & issue: Vol. 13

Abstract

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In the present study, 2D Poisson-type equation is solved by a meshless Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The influence of the kernel function, smoothing length and particle discretizations of problem domain on the solutions of Poisson-type equations is investigated. Compared with other kernel functions, the cubic B-spline kernel function shows good capacity to reproduce a complicated function value and its first and second derivatives, when the smoothing length is chosen as 1.1 times the particles’ distance. Several types of Poisson equations are solved by SSPH method, and the numerical results exhibit a very good accuracy when comparing with the analytical solutions. Keywords: Smoothed Particle Hydrodynamics, Poisson equation, Helmholtz, Kernel function

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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