Numerical approximations of darcian flow through unsaturated soil

The choice of appropriate intrablock approximations for the unsaturated hydraulic conductivity is a critical step for the numerical solution of Richards equation. Forms commonly used include arithmetic, geometric and harmonic averaging. The choice is most often based on convenience and custom. This study presents a framework for comparing any scheme for weighting the unsaturated hydraulic conductivity against the correct Darcian flow across a block for steady conditions. Such comparisons are carried out for a number of commonly used averages, and errors are shown to be alarmingly high in some cases. A scheme for approximately matching the correct Darcian flux is illustrated by two infiltration examples. In the first, the arithmetic and weighted schemes are superior to the geometric average when compared to a quasi‐analytical solution. For the second example, the weighted solution is slightly better than either the arithmetic or geometric averaging schemes. These examples also illustrate that an acceptable mass balance should not be used as a sole criterion for success as it can probably be attained with most schemes. The conclusions are believed relevant for algorithms which are pressure head based, water content based or other choices and for multidimensional as well as one‐dimensional flow problems.