Implicit TVDLF Methods for Diffusion and Kinematic Flows

Abstract

Diffusion-wave and kinematic-wave approximations of the St. Venant equations are commonly used in physically based, regional hydrologic models because they have high computational efficiency and use fewer equations. Increasingly, models based on these equations are being applied to cover larger areas of land with different surface and groundwater regimes and complicated topography. Existing numerical methods are not well suited for multiyear simulation of detailed flow behavior unless they can be run efficiently with large time steps and control numerical error. A numerical method also should be able to solve both diffusive and kinematic wave models. A total variation diminishing Lax-Friedrichs type method (TVDLF) that is stable and accurate with both diffusive- and kinematic-wave models and large time steps is presented as a means to address this problem. It uses a linearized conservative implicit formulation that makes it possible to avoid nonlinear iterations. The numerical method was tested successfully using steady flow profiles, analytical solutions for wave propagation, and observed data from a field experiment in a mountain stream of Sri Lanka. A grid convergence test and an error analysis are carried out to determine how the model errors of the numerical schemes behave with the discretization.