Analytical solution to a diffusion wave equation with variable coefficients for overland flow

Abstract

Urban areas are often covered by materials with smooth ground surface and poor water permeability, which may cause problems such as increasing flow velocity and discharge.This study employed the diffusion wave equation to investigate the variation of overland flow, and analytical solutions were obtained by the generalized integral transformation technique. Examining previous research, we found when the coefficients in the diffusion wave equation were treated as constants, the simulated results would be mass non-conservative. This study corrected the coefficients which makes the flow meet the mass conservation law to improve the simulation results. An alternative solution to the overland flow considering time-varying rainfall and infiltration were proposed and the results were well compared with previous numerical solutions and experimental data.