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ISSN : 1226-0657

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Vol.6 No.2

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1999, v.6 no.2, pp.113-120
Bestman, A.R.
Odigi, M.I.
Bestman,, A. , & Odigi,, M. (1999). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 6(2), 113-120.

Abstract

This paper studies the problem of an infinite confined aquifer which at time t ＜ 0 is assumed motionless. At time t = 0 crude oil seeps into the aquifer, thereby contaminating the valuable drinking water. Since the crude oil and water are im-miscible, the problem is posed as a one-dimensional two-phase unsteady moving boundary problem. A similarity solution is developed in which the moving front parameter is obtained by Newton-Ralphson iteration. A numerical scheme, involving the front tracking method, is devised employing the fourth order Runge-Kutta method. Comparison of the exact and numerical schemes shows an error of only 3%. Thus the developed numerical scheme is quite accurate in tackling more realistic problems where exact solutions are not possible.

keywords
aquifer, fourth order Runge-Kutter method

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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