||General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation.
Celia, M. A. ;
Bouloutas, E. T. ;
Zarba, R. L. ;
||Princeton Univ., NJ. Dept. of Civil Engineering and Operations Research. ;Camp, Dresser and McKee, Inc., Boston, MA.;Robert S. Kerr Environmental Research Lab., Ada, OK.;Nuclear Regulatory Commission, Washington, DC.;National Science Foundation, Washington, DC.
||NRC-04-88-074, NSF-8657419-CES; EPA/600/J-90/445;
Flow equations ;
Computational fluid dynamics ;
Partial differential equations ;
Numerical integration ;
Ground water ;
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The paper investigates the numerical behavior of standard approximation methods for the unsaturated flow equation. Solution using the h-based formulation and a backward Euler time discretization is shown to produce unacceptably large mass balance errors for many example calculations. This is true for any iteration method (Picard, Newton-Raphson, etc.). It is also true for both finite difference and finite element approximations in space, although finite elements are generally inferior to finite differences. A modified numerical approach is proposed that alleviates the mass balance problems discussed above. This approach is based on a fully implicit (backward Euler) time approximation applied to the mixed form of the unsaturated flow equation.