Abstract
This work studies a nonsaturated flow and the heat transfer associated phenomenon of a newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, included to account for the compressibility of the system as a whole. A set of four nonlinear partial differential equations describe the problem whose hydrodynamical part is approximated by means of a Glimm's scheme combined with an operator splitting technique.
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Saldanha da Gama, R., Martins-Costa, M. Incompressible fluid flow and heat transfer through a nonsaturated porous medium. Computational Mechanics 20, 479–494 (1997). https://doi.org/10.1007/s004660050269
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DOI: https://doi.org/10.1007/s004660050269