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.
Figure1. Initial profile
Figure2. Solution in time t=0.05
Figure3. Solution in time t=0.10
Figure4. Solution in time t=0.20
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