Diffusive Wave Flood Routing Problem with Lateral Inflow
Manotosh Kumbhakar, Vijay P. Singh · 2023
This chapter discusses three kinds of series solutions for the diffusive wave equation with lateral inflow or outflow. The series solutions are developed using HAM, HPM, and OHAM. Moussa derived an analytical solution to a similar equation using the Laplace transform. It is found that HAM- and OHAM-based solutions can satisfactorily produce an accurate solution to the diffusion equation. OHAM provides an accurate solution with just three terms of the series. On the other hand, HPM does not provide an accurate solution, perhaps because of the choice of initial approximation and linear operator. The discussion shows the potential of HAM and OHAM in the context of obtaining a series solution that is valid over a wide range of the domain. The theoretical and numerical convergences of the series solutions are provided.