Two-phase flow in porous media

We solve doubly nonlinear degenerate parabolic problem

u_t = div (grad ( b(u))

where b(u)=u^2/(u^2+0.5 (1-u)^2) is the so-called Buckley-Leverett function with two points of degeneracies (u=0, u=1) In figures we present evolution of the solution in time moments t=0, t=0.05, t=0.10, t=0.20, respectively. The interface at the level u=1 is shrinking and the interface at the level u=0 is expanding. Such phenomenon models e.g. mixing of oil and water in two phase flow in porous media.


Picture1

Figure1. Initial profile


Picture2

Figure2. Solution in time t=0.05


Picture3

Figure3. Solution in time t=0.10


Picture4

Figure4. Solution in time t=0.20


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