| Abstrakt: |
In this paper we consider the singular boundary value problem, −z1/pz″=Df/1+p for 00 and D: [0,1]→R is a given function. This problem arises in a model for two-phase capillary induced flow in porous media. Considering the special case Df=fαw1−fα0, with α0,αw>−2, we investigate the singular behaviour of the solution zf as α0,αw↓−2. We show that the solution then becomes unbounded. We investigate the behaviour of z and z′ in this limit process. The results are incorporated in an algorithm which we use to solve the problem numerically. The numerical results show significant improvement over standard discretisation techniques near the limit. Non-existence arises for α0or αw≤−2. |
