Two‐phase flows in karstic geometry

Abstract

Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications.In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been done on multi-phase flows in karstic geometry.In this paper we present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. Uniquely solvable first and second order in time numerical schemes that preserve the associated energy law are presented as well.

Experimental and Numerical Study of Evaporation From Wavy Surfaces by Coupling Free Flow and Porous Media Flow

“…But when multiphases are involved, two‐domain approach is physical and accurate. This two‐domain approach has been successfully used in multiphase coupling free‐flow and porous‐media flow problems (Baber et al, ; Davarzani et al, ; Han et al, ; Mosthaf et al, ; Tezduyar et al, ; Vanderborght et al, ).…”

Uniquely solvable and energy stable decoupled numerical schemes for the Cahn–Hilliard–Stokes–Darcy system for two-phase flows in karstic geometry

“…We show that both decoupled numerical schemes are uniquely solvable, energy stable, and mass conservative. Ample numerical results are presented to demonstrate the accuracy and efficiency of our schemes.Keywords Cahn-Hilliard-Stokes-Darcy system · two phase flow · karstic geometry · interface boundary conditions · diffuse interface modelMany natural and engineering applications involve multiphase flows in karstic geometry, i.e., geometry with both conduit (or vug) and porous media [25]. Such kind of problems are intrinsically difficulty due to the multi-scale multi-physics nature.…”

“…Such kind of problems are intrinsically difficulty due to the multi-scale multi-physics nature. In [25], the authors utilized Onsager's extremum principle to derive a diffuse interface model, the so-called Cahn-Hilliard-Stokes-Darcy system (CHSD), for two-phase incompressible flows with matched densities in the karstic geometry. Existence and weak-strong uniqueness of weak solutions for the CHSD system have been proved recently in [28].…”

“…Many natural and engineering applications involve multiphase flows in karstic geometry, i.e., geometry with both conduit (or vug) and porous media [25]. Such kind of problems are intrinsically difficulty due to the multi-scale multi-physics nature.…”

“…Decoupled Energy-stable Numerical Schemes for CHSD 5 The CHSD System is subject to the following boundary and interface boundary conditions. We refer to [25] for the detailed derivation of the CHSD model (1.1)-(1.6) together with the interface boundary conditions (1.10) - (1.14). The last interface condition (1.14) is the so-called Beavers-Joseph-Saffman-Jones (BJSJ) condition (cf.…”