Degenerate Two-Phase Incompressible Flow

Local Mesh Refinement for Degenerate Two-phase Incompressible Flow Problems

In this paper we consider nite element methods for a degenerate elliptic-parabolic partial diierential system which describes the ow of two incompressible, immiscible uids in porous media. Local mesh reenement techniques for solving this degenerate system are discussed. 1. TWO-PHASE FLOW EQUATIONS In this paper we consider nite element methods for the ow of two incompressible, immiscible uids i...

Degenerate Two - Phase In ompressible Flow

3D Incompressible Two-Phase Flow Benchmark Computations for Rising Droplets

We perform 3D incompressible two-phase flow simulations of rising droplets. Based on a similar 2D benchmark, a 3D benchmark configuration with two test cases is formulated in which we compare the flow solvers DROPS, NaSt3DGPF and OpenFOAM. All codes adopt different numerical techniques. We define several quantities of interest and investigate their temporal evolution in both test cases. For mos...

Mathematical Properties of Nonhyperbolic Models for Incompressible Two-Phase Flow

Many models for multi-fluid flow result in equations which fail to be hyperbolic. One example is one-dimensional flow of an incompressible two-phase fluid. In the simplest model, the principal part of the differential operator has characteristics with nonzero imaginary part for any state of the fluid which contains both phases. Thus, the linearized equations are catastrophically unstable. This ...

Homogenization of the degenerate two-phase flow equations

We analyze two-phase flow in highly heterogeneous media. Problems related to the degeneracy of the permeability coefficient functions are treated with a new concept of weighted solutions. Instead of the pressure variables we formulate the problem with the weighted pressure function ψ, which is obtained as the product of permeability and pressure. We perform the homogenization limit and obtain e...