||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 ;
||Most EPA libraries have a fiche copy filed under the call number shown. Check with individual libraries about paper copy.
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.