Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5016500 | International Journal of Non-Linear Mechanics | 2017 | 38 Pages |
Abstract
This work proposes a mathematical model to study the filling up of an unsaturated porous medium by a liquid identifying the transition from unsaturated to saturated flow and allowing a small super saturation. As a consequence the problem remains hyperbolic even when saturation is reached. This important feature enables obtaining numerical solution for any initial value problem and allows employing Glimm's scheme associated with an operator splitting technique for treating drag and viscous effects. A mixture theory approach is used to build the mechanical model, considering a mixture of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and a very low-density gas (to account for the mixture compressibility). The constitutive assumption proposed for the pressure gives rise to a continuous function of the fluid fraction. The complete solution of the Riemann problem associated with the system of conservation laws, as well as four examples, considering all the four possible connections, namely, 1-shock/2-shock, 1-rarefaction/2-rarefaction, 1-rarefaction/2-shock and 1-shock/2-rarefaction are presented.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Mechanical Engineering
Authors
Maria Laura Martins-Costa, Dario Monte Alegre, Felipe Bastos de Freitas Rachid, Luiz Guilherme C.M. Jardim, Rogério M. Saldanha da Gama,