Two-phase porous media flows with dynamic capillary effects and hysteresis: uniqueness of weak solutions

DOI10.1016/j.camwa.2015.02.009zbMath1443.76211OpenAlexW1980980490MaRDI QIDQ2006050

Yanyan Li

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.02.009

zbMATH Keywords

hysteresisweak solutionuniquenesstwo-phase flowdynamic capillary pressure

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Multiphase and multicomponent flows (76T99)

Related Items

Existence and properties of solutions of the extended play-type hysteresis model ⋮ Capillary hysteresis and gravity segregation in two phase flow through porous media ⋮ Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media ⋮ Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity ⋮ Degenerate two-phase porous media flow model with dynamic capillarity ⋮ Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure ⋮ Global well-posedness for a fourth order pseudo-parabolic equation with memory and source terms ⋮ Approximation of hysteresis functional ⋮ A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models ⋮ Homogenized model of two-phase flow with local nonequilibrium in double porosity media ⋮ Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects ⋮ Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis ⋮ Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media ⋮ Linearly compact scheme for 2D Sobolev equation with Burgers' type nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• The Richards equation with hysteresis and degenerate capillary pressure
• Uniqueness of weak solutions for a pseudo-parabolic equation modeling two phase flow in porous media
• Differential models of hysteresis
• Flow of oil and water in a porous medium
• Travelling wave solutions for degenerate pseudo-parabolic equations modelling two-phase flow in porous media
• A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure
• Pseudoparabolic regularization of forward-backward parabolic equations: a logarithmic nonlinearity
• Linear and quasilinear elliptic equations
• An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
• A class of pseudo-parabolic equations: existence, uniqueness of weak solutions, and error estimates for the Euler-implicit discretization
• Elliptic Partial Differential Equations of Second Order
• Two-phase flow equations with a dynamic capillary pressure
• Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution