The Buckley-Leverett Equation with Dynamic Capillary Pressure

Details The Buckley-Leverett Equation with Dynamic Capillary Pressure The Buckley-Leverett Equation with Dynamic Capillary Pressure

2010-09-02

arxiv.org/abs/1009.0467v2

Mathematics

Analysis of PDEs

This paper has been withdrawn by the author because it is now published in SIAM J. Appl. Math 71(4) pp. 1088-1108

Scientific paper

The Buckley-Leverett equation for two phase flow in a porous medium is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear pseudo-parabolic partial differential equation. Phase plane analysis, including a separation function to measure the distance between invariant manifolds, is used to determine when the equation supports traveling waves corresponding to undercompressive shocks. The Riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation.

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