A numerical study of the applicability of the Boussinesq approximation for a fluid-saturated porous medium.

*(English)*Zbl 0575.76089The regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid-saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water-saturated porous region.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76R10 | Free convection |

76M99 | Basic methods in fluid mechanics |

##### Keywords:

finite element; Boussinesq approximation; fluid-saturated porous medium; perturbation method; continuity relation
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\textit{D. K. Gartling} and \textit{C. E. Hickox}, Int. J. Numer. Methods Fluids 5, 995--1013 (1985; Zbl 0575.76089)

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