Numerical Solution of the Continuity Equation for Soil Water Flow Using Precomputed Steady-State Fluxes

Numerical methods of calculating water flow in soils usually rely on solving Richards9 equation, which is obtained by combining the equation of continuity with Darcy9s law for water fluxes. In this study, the one-dimensional equation of continuity was solved using tables of precomputed steady-state fluxes read from disk. This results in simpler and faster code for applications such as field water balance models, which may use relatively large depth spacings and many repeated calculations. There is no speed penalty for the use of more complex property descriptions. Steady-state flux tables were computed by integration of Darcy9s law, which results in the same solution as Richards9 equation, but in principle they could be obtained in some other way. The method is much faster and more stable than conventional iterative methods both because it is noniterative and because good estimates of steady-state fluxes allow accurate solutions with larger vertical grid spacings, which in turn allow larger time steps. It is also both faster and simpler than other noniterative methods that provide good flux estimates because the fluxes are already available without the extra code and the time needed to compute them.