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Volume 5, Issue 5
Numerical Methods for Unsaturated Flow with Dynamic Capillary Pressure in Heterogeneous Porous Media

M. Peszynska & S.-Y. Yi

Int. J. Numer. Anal. Mod., 5 (2008), pp. 126-149.

Published online: 2018-11

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  • Abstract

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' 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.

  • AMS Subject Headings

35K65, 35K70, 65M06, 76S05

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-126, author = {Peszynska , M. and Yi , S.-Y.}, title = {Numerical Methods for Unsaturated Flow with Dynamic Capillary Pressure in Heterogeneous Porous Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {5}, number = {5}, pages = {126--149}, abstract = {

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' 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/844.html} }
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 -

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' 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.

M. Peszynska & S.-Y. Yi. (1970). Numerical Methods for Unsaturated Flow with Dynamic Capillary Pressure in Heterogeneous Porous Media. International Journal of Numerical Analysis and Modeling. 5 (5). 126-149. doi:
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