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| Buckley-Leverett (MBL) equation describes two-phase flow in porous
media. The MBL equation differs from the classical Buckley-Leverett
(BL) equation by including a balanced diffusive-dispersive combination. The
dispersive term is a third order mixed derivatives term, which models
the dynamic effects in the pressure difference between the two phases.
The classical BL equation gives a monotone water saturation profile
for any Riemann problem; on the contrast, when the dispersive
parameter is large enough, the MBL equation delivers non-monotone
water saturation profile for certain Riemann problems as suggested by
the experimental observations. In this talk, we show that the solution
of the finite interval $[0,L]$ boundary value problem converges to
that of the half-line $[0,+\infty)$ boundary value problem expoentially fast for the MBL equation as $L\rightarrow +\infty$. In this talk, I will discuss both the
analytical and numerical results for the MBL equation. (This is a
joint work with Chiu-Yen Kao.) |
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