Dynamic Time Step for One-Dimensional Overland Flow Kinematic Wave Solution

Abstract

Kinematic wave theory is widely used in modeling a variety of hydrologic processes. Results of applying the kinematic wave overland flow solution using different time steps showed that the conventionally used stability criterion known as the Courant condition fails to give a time step estimate that ensures stable and accurate numerical solutions. Accordingly, a new accuracy-based dynamic time step estimate for the one dimensional overland flow kinematic wave solution is developed. The newly developed dynamic time step estimates are functions of the mesh size, watershed slope, roughness, excess rainfall, and time of concentration. The new criteria were developed by comparing the consistent formulation of the Galerkin-Crank Nicholson numerical solution of the kinematic wave equation to the characteristic method-based analytical solution, using different time steps and meshes. For each simulation, characterized by boundary and initial conditions and mesh size, an optimal time step that integrates the problem within 5% error was determined. The series of mesh sizes and corresponding optimal time steps were used to develop the dynamic time step. The time step criteria were tested on a variety of problems, including a steady state and time varying rainfall scenarios, and proved to be adequate for accurate and stable results within an efficient computational time. The criteria can be easily integrated in flow routing models to select the optimal time step with minimal user input.