TY - JOUR
T1 - Numerical Methods for Unsaturated Flow with Dynamic Capillary Pressure in Heterogeneous Porous Media
AU - Peszynska , M.
AU - Yi , S.-Y.
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 126
EP - 149
PY - 2018
DA - 2018/11
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/844.html
KW - unsaturated flow, Richards’ equation, two-phase flow model, dynamic capillary pressure, pseudo-parabolic equation, finite difference method,
locally conservative Eulerian-Lagrangian method, implicit time-stepping.
AB - <p style="text-align: justify;">Traditional unsaturated flow models use a capillary
pressure-saturation relationship determined under static conditions.
Recently it was proposed to extend this relationship to include dynamic
effects and in particular flow rates. In this paper, we consider
numerical modeling of unsaturated flow models incorporating dynamic
capillary pressure terms. The resulting model equations are of nonlinear
degenerate pseudo-parabolic type with or without convection terms, and
follow either Richards&#39; equation or the full two-phase flow model. We
systematically study the difficulties associated with numerical
approximation of such equations using two classes of methods, a
cell-centered finite difference method (FD) and a locally conservative
Eulerian-Lagrangian method (LCELM) based on the finite difference
method. We discuss convergence of the methods and extensions to
heterogeneous porous media with different rock types. In
convection-dominated cases and for large dynamic effects instabilities
may arise for some of the methods while those are absent in other cases.</p>