Unsaturated deformable porous media flow with thermal phase transition

0481815 - MÚ 2018 RIV SG eng J - Journal Article
Krejčí, Pavel - Rocca, E. - Sprekels, J.
Unsaturated deformable porous media flow with thermal phase transition.
Mathematical Models and Methods in Applied Sciences. Roč. 27, č. 14 (2017), s. 2675-2710. ISSN 0218-2025. E-ISSN 1793-6314
R&D Projects: GA ČR(CZ) GA15-12227S
Institutional support: RVO:67985840
Keywords : porous media * phase transitions * existence of solutions
OECD category: Applied mathematics
Impact factor: 3.319, year: 2017
http://www.worldscientific.com/doi/abs/10.1142/S0218202517500555

In this paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid–solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius–Duhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions are proved by means of cut-off techniques and suitable Moser-type estimates.
Permanent Link: http://hdl.handle.net/11104/0277287