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A conservative and consistent Lagrangian gradient smoothing method for simulating free surface flows in hydrodynamics

  • Zirui MaoEmail author
  • G. R. Liu
  • Xiangwei Dong
  • Tao Lin
Article

Abstract

A novel particle method, Lagrangian gradient smoothing method (L-GSM), has been proposed in our earlier work to avoid the tensile instability problem inherently existed in SPH, through replacing the SPH gradient operator with a robust GSM gradient operator. However, the nominal area of each L-GSM particle determined by the relative location of particles is always inconsistent with the real representative area of it in simulation, especially in large-deformation problems. This is why the earlier L-GSM model has to be limited to the solid-like flow simulations where the deformation is not very serious. In this work, a conservative and consistent Lagrangian gradient smoothing method (CCL-GSM) is developed for handling large-deformation problems in hydrodynamics with an arbitrarily changing free surface profile. This is achieved by deriving a conservative and consistent form for the discretized Navier–Stokes governing equations in L-GSM, which even holds in the neighbor-updating or ‘remeshing’ process. Special techniques are also devised for free surface treatment, which is important to restore the conservation and consistency manner of CCL-GSM simulation on free surface boundary. The effectiveness of the proposed CCL-GSM framework is evaluated with a number of benchmarking examples, including dam break, wall impacts of breaking dam, water discharge and water splash. It shows that the CCL-GSM model can handle the incompressible flows with complicated free surfaces effectively and easily. The results comparison with experiments and SPH solutions demonstrates that the CCL-GSM can give a desirable result for all these examples.

Keywords

Conservative and consistent Lagrangian gradient smoothing method L-GSM SPH Free surface flows Incompressible flows Hydrodynamics 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© OWZ 2019

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiCincinnatiUSA
  2. 2.Taiyuan University of TechnologyTaiyuanChina
  3. 3.College of Mechanical and Electronic EngineeringChina University of PetroleumQingdaoChina

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