On consistency and energy conservation in smoothed particle hydrodynamics

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.