Turbulent flow in porous media
We solve doubly nonlinear degenerate parabolic problem
u_t = div (|grad(u^m)|^(p-1) grad(u^m))
where m, p are positive constants, modeling the porous media flow of a gas in turbulent (p<1) regime using the so-called p-Laplacian.
We present time evolution of the solution with parameters m=6, p=0.5. The solution is plotted in time moments t=0, t=0.05, t=0.10, t=0.14. One can see successive filling of the inner wedge with the waiting time in the center point (the numerical waiting time is 0.11). The outer interface of the solution is practically not moving during the computed time because of the strong degeneracy (m=6).
Figure1. Initial profile
Figure2. Solution and its cut in time t=0.05
Figure3. Solution and its cut in time t=0.10
Figure4. Profile of solution in time t=0.14, filling of the vedge
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