Abstract
Van Duijn, C.1. and F.J.T. Floris, On a singular diffusion equation originating from porous media flow, Asymptotic Analysis 10 (1995) 29-48. In this paper we consider the singular boundary value problem, -zl/pzII = D(f)/(l +p) for 0 0 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 D(f) = jC'w (1- f)a o , with 00 0 , Q w > -2, we investigate the singular behaviour of the solution z(f) as Qo,QwL - 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 00 0 or Qw :( -2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.