SIMULATION OF A FLOW THROUGH A RIGID POROUS MEDIUM SUBJECTED TO A CONSTRAINT

Abstract

This work uses a previuosly proposed mathematical model to study the filling up of an unsaturated rigid porous medium by a liquid identifying the transition from unsaturated to saturated flow. This model accounts for the physical upper bound of the fluid fraction that depends on the volume of the pores and employs a mixture theory to describe the flow. The mathematical description of the phenomenon leads to a nonlinear hyperbolic system. In order to solve this system, the space of admissible solutions must be enlarged to admit discontinuous solutions that may be shock waves. The complete solution of a Riemann problem associated to the system of conservation laws satisfying the constraint given by the saturation upper bound is presented. Some meaningful results are presented and discussed.