Conservative characteristics-based schemes for mass transport

Backward-characteristics schemes for solution of the mass transport equation are inherently nonconservative when the advective velocity is variable, and they have difficulties at boundaries where mass flux conditions are imposed. Also, they generally produce over- and undershoots of the solution or are not accurate enough if a sharp front exists. To circumvent these shortcomings, higher-order-characteristics schemes based on a minimax criterion are developed. The finite-difference expressions of these schemes are then modified to follow a flux-transport form, and a flux limiter is added to the schemes. The resulting schemes are accurate in simulating mass transport in saturated-unsaturated flow in which sharp fronts exist, the velocity is variable, and the flux boundary condition is imposed.