New Solution of Two Dimensional Shallow Water Equations by Modified Laplace Decomposition Method

In this paper, an accurate semi-analytical solution of the full nonlinear two dimensional shallow water equations including friction effects is obtained through the modified Laplace decomposition method. The equations are commonly used in the study of shallow water currents and waves in the rivers and the marine environments as an accurate model that closely describes the relevant dynamics of flow. To do so, first, the Laplace transforms are applied to the SWEs while the decomposition method (DM) is used for nonlinear terms and finally, appropriate Pade approximants are applied to improve the stability of the solution at large times. Our results demonstrate that the method is very effective due to provision of an accurate solution for the SWEs with the least computational cost and without the need for linearization or discretization. Besides, a comparison with the variational iteration method is also provided. Numerical and graphical illustrations of the flow depth and the velocities and the time evolution of the residual values of which, as an index of the solution error for a given application are presented and show that the proposed method can provide an accurate flow response on a long time horizon.

Keywords:

Semi-analytical solution , Two dimensional shallow water equations , Fluid flow behavior , Laplace decomposition method , Pade approximant.