MODIFICATION OF WELGE'S METHOD OF SHOCK FRONT LOCATION IN THE BUCKLEY-LEVERETT PROBLEM FOR NONZERO INITIAL CONDITION.

In the analytical solution of the Buckley-Leverett problem, H. J. Welge recommends that to locate a front, one should draw a tangent to the fractional saturation curve from the origin. In this paper I establish that this procedure will be correct only for the case of a zero initial condition. For a nonzero initial condition, a mass-conserving front will be located farther down the flow direction. The implications of this finding for error analysis in comparing numerical solutions to the analytical one are discussed.