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

The objective of this paper was to provide a modification to the Welge's method for an appropriate location of the shock-front on the basis of mass conservation for non-zero initial condition. Analytical solution to the Bucklely-Leverett equation is known to yield a multiple-valued saturation profile which is resolved by locating a shock front on the basis of mass conservation. A quick way of locating the front was provided by Welge. Welge's method locates the front accurately for the particular case when the initial saturation is zero over the entire space domain. In the more general case of a non-zero initial condition the method needs general case of a non-zero initial condition the method needs modification. One such method is presented in this paper.