ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract When both the diffusivityD and fractional flow functionf have a power law dependence on the water content θ, i.e.D=D oθα andf=θα+1, the nonlinear transport equation for radially symmetric two phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary conditionV wo and comparison with experimental data are given. In particular, when the fluxV wo and a are related byV wo(α + 1)/D o=2, a new fully explicit analytical solution is found as θ(r, t)=(1 − αr 2/4D ot)1/α forr 2 〈 4D ot/α and θ(r, t)=0 forr 2 ≥ 4D ot/α We show that the existence of this exact soution is due to the presence of a Lagrangian symmetry.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00952080
Permalink