Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media †. Holmes, D.; Williams, J.; and Tilke, P International Journal for Numerical and Analytical Methods in Geomechanics, 35:419-437, 0.
abstract   bibtex   
In this paper, a three-dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale \textdegreeuid \textdegreeow in porous media is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including, the characterization of flow through permeable rock for both groundwater and petroleum reservoir research. SPH provides the means to model complex multi-phase \textdegreeows through such media however acceptance of the methodology has been hampered by the apparent lack of actual veri\textasciimacroncation within the literature, particulary in the three- dimensional case. In this paper, the accuracy of SPH is addressed via a comparison to the previously recognized benchmarks of authors such as Sangani and Acrivos (1982), Zick and Homsy (1982) and Larson and Higdon (1989) for the well defined classical problems of flow through idealized two- and three-dimensional porous media. The accuracy of results for such low Reynolds number flows is highly dependent on the implementation of no-slip boundary conditions. A new, robust, and numerically e\textpmcient, method for implementing such boundaries in SPH is presented. Simulation results for friction coe\textpmcient and permeability are shown to agree well with the available benchmarks.
@article{Holmes_Smooth,
  pages={419-437},
  author={Holmes, {D.W.} and Williams, {J.R.} and Tilke, P},
  title={Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media †},
  abstract={In this paper, a three-dimensional smooth particle hydrodynamics {(SPH)} simulator for modeling grain scale {\textdegree}uid {\textdegree}ow in porous media is presented. The versatility of the {SPH} method has driven its use in increasingly complex areas of flow analysis, including, the characterization of flow through permeable rock for both groundwater and petroleum reservoir research. {SPH} provides the means to model complex multi-phase {\textdegree}ows through such media however acceptance of the methodology has been hampered by the apparent lack of actual veri{\textasciimacron}cation within the literature, particulary in the three- dimensional case. In this paper, the accuracy of {SPH} is addressed via a comparison to the previously recognized benchmarks of authors such as Sangani and Acrivos (1982), Zick and Homsy (1982) and Larson and Higdon (1989) for the well defined classical problems of flow through idealized two- and three-dimensional porous media. The accuracy of results for such low Reynolds number flows is highly dependent on the implementation of no-slip boundary conditions. A new, robust, and numerically e{\textpm}cient, method for implementing such boundaries in {SPH} is presented. Simulation results for friction coe{\textpm}cient and permeability are shown to agree well with the available benchmarks.},
  journal={International Journal for Numerical and Analytical Methods in Geomechanics},
  year={0},
  volume={35},
  keywords={consolidated porous media
friction coefficient
no-slip boundary conditions
permeability
smooth particle hydrodynamics}
}
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