Obtaining gradually varied flow profile in trapezoidal and triangular channels using semi-analytical method of Adomian decomposition

The non-uniform flow in a prismatic channel with gradual changes in the free water surface level is called the gradually varied flow (GVF). Calculation of the GVF profiles over the last century has become a significant topic for the researchers in the relevant fields.  To obtain this profile, the nonlinear ordinary differential equation of the GVF needs to be solved. This can be carried out either numerically or analytically. Although several studies have been conducted on the GVF in open channels in various forms (Jan & Chen, 2013; Vatankhah, 2010, 2015; Homayoon & Abedini, 2019), the number of semi-analytical studies in the field of gradual variable flow in trapezoidal and triangular channels is limited, which requires further investigation. In this research, the Adomian Decomposition Method (ADM) is used to find a semi-analytical solution for solving the GVF equation in the triangular and trapezoidal prismatic channels. In this method, the Manning equation is used as the resistance equation. Moreover, for the aim of verifying the semi-analytical solutions, the ADM results are compared with the finite difference method (FDM). The presented semi-analytical solutions in this paper can be used to validate other numerical methods in similar studies.