A mathematical model for the multiscale process of filtration of weakly compressible liquids and gases in periodic porous media is proposed with reference to the process of composite material production based on the RTM method. Using the method of asymptotic averaging made it possible to formulate the so-called local filtration problems for a single pore and the global problem of unsteady filtration of weakly compressible liquids. Two models of a weakly compressible fluid are considered: classical and generalized. The classical model is based on the Musket’s equation of the state, which requires initial constant values for fluid pressure and density to be preset. The generalized model is based on the same equation, but requires presetting only the initial fluid density, using the unknown hydrostatic pressure instead of the initial constant liquid pressure. The results of simulation of the impregnation process of a of filler material sample by a binder are presented using the two models of a weakly compressible liquid.
Dimitrienko Yu. I.Bogdanov I.O. Multiscale modeling of liquid binder filtration processes in composite structures manufactured by RTM Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 3-27