Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media
نویسندگان
چکیده
Mathematical modeling of fluid flow in a porous medium is usually described by continuity equation and chosen constitutive law. The latter, depending on the problem at hand, may be nonlinear relation between fluid's pressure gradient velocity. actual shape this normally outset problem, even though, practice, experience velocities outside its range applicability. We propose here an adaptive model, so that most appropriate law locally selected computed From analytical point view, we show well-posedness when monotone velocity existence one space dimension otherwise. computational present new approach based regularizing via mollification underlying dissipation, i.e., power lost to through drag. resulting regularization shown converge original using Γ-convergence dissipation case. This gives rise variational numerical scheme which applies very general problems validate three test cases.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2023
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111844