Fast numerical approach for solving a problem of filtration of viscoelastic fluid in porous media
Miglena N. Koleva · AIP conference proceedings · 2022
The paper concerns two-phase problem, describing filtering a viscous incompressible fluid in a deformable porous medium, assuming that the poroplastic medium has both viscous and elastic properties. We develop fast and accurate numerical algorithm for solving initial-boundary value problem for reduced system of two equations for effective pressure and porosity. The proposed discrete scheme preserves the physical properties of the solution. The system is approximated implicitly, but we solve the discrete problem such that to avoid iteration process and to attain second order of convergence in space and time. Computational results are presented and discussed.