5 research outputs found
On the sufficient conditions for the S-shaped Buckley-Leverett function
The flux function in the Buckley-Leverett equation, that is, the function
characterizing the ratio of the relative mobility functions of the two phases,
is considered. The common conjecture stating that any convex mobilities result
in an S-shaped Buckley-Leverett function is analyzed and disproved by a
counterexample. Additionally, sufficient conditions for the S-shaped
Buckley-Leverett function are given. The class of functions satisfying those
conditions is proven to be closed under multiplication. Some functions from
known relative mobility models are confirmed to be in that class
On uniqueness in Steiner problem
We prove that the set of -point configurations for which solution of the
planar Steiner problem is not unique has Hausdorff dimension is at most .
Moreover, we show that the Hausdorff dimension of -points configurations on
which some locally minimal trees have the same length is also at most .
Methods we use essentially requires some analytic structure and some
finiteness, so that we prove a similar result for a complete Riemannian
analytic manifolds under some apriori assumption on the Steiner problem on
them
Relation between size of mixing zone and intermediate concentration in miscible displacement
We investigate the miscible displacement of a viscous liquid by a less
viscous one in a porous medium, which frequently leads to the formation of a
mixing zone characterized by thin fingers. The mixing zone grows in time due to
the difference in speed between the leading and trailing edges. The transverse
flow equilibrium (TFE) model provides estimates of these speeds. We propose an
enhancement for the TFE estimates. It is based on the assumption that an
intermediate concentration exists near the tip of the finger, which allows to
reduce the integration interval in the speed estimate. Numerical simulations of
the computational fluid dynamics model were conducted to validate the new
estimates. The refined estimates offer greater accuracy than those provided by
the original TFE model.Comment: 16 pages, 11 figure