Premium
On consistency and energy conservation in smoothed particle hydrodynamics
Author(s) -
Islam Md Rushdie Ibne,
Chakraborty Sukanta,
Shaw Amit
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5937
Subject(s) - smoothed particle hydrodynamics , energy conservation , consistency (knowledge bases) , conservation of energy , benchmark (surveying) , term (time) , norm (philosophy) , mathematics , mathematical optimization , conservation law , function (biology) , particle (ecology) , computer science , mechanics , physics , mathematical analysis , geometry , engineering , oceanography , geology , geodesy , quantum mechanics , evolutionary biology , biology , political science , geography , law , electrical engineering , thermodynamics
Summary Energy conservation and consistency are not easy to achieve simultaneously in smoothed particle hydrodynamics (SPH). In this study, an efficient strategy is proposed to achieve energy conservation in an SPH framework with a consistent basis function. Herein, at every particle pair interaction, a correction term is introduced such that energy conservation is restored locally and, at the same time, the total variation of different variables due to the correction term is minimum. The final form of the proposed formulation is such that no additional computational effort is required and the simplicity of SPH is preserved. The theoretical error estimate of the proposed formulation is performed. The proposed scheme is also compared with benchmark SPH formulations in terms of the L 2 error norm for representative functional derivatives both in regular and irregular particle distributions. Finally, the efficacy of the proposed formulation in conserving energy and maintaining accuracy is demonstrated via few elastic, elastic‐plastic impact and fracture problems.