Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water

Abstract

This study aims to investigate the capability of two common numerical methods, Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM), and to suggest more efficient approximate solution method to the governing equations of nonlinear surface wave propagation in shallow water. To do so, semi-flat, moderate, and sharp slope of shore which are connected to an open ocean with a uniform depth are exposed to a solitary wave with initial wave height H=2 and stationary elevation d=20. Then, the surface elevation and velocity curves for these profiles are determined and compared by HAM and VIM. To verify the numerical modeling, two slopes i.e. semi-flat and moderate slope are considered and modeled in Flow-3D. Afterwards, the results of surface elevations are compared to each other by using correlation coefficient. The correlation coefficients for the slopes represent that the results coincide well. Ultimately, although the results of both methods are quite similar, using HAM is highly recommend rather than VIM since it makes solution procedure fast-converging and more abridged.

Keywords

• homotopy analysis method (ham)
• variational iteration method (vim)
• shallow water equations