Comparative Analysis of Finite Difference Methods for Coupled Surface and Subsurface Flows in Extended Shallow Water Equations
Abstract
Numerical simulation of coupled surface and subsurface flows is crucial for modeling equations for flood waves, runoff processes, and tsunami wave propagation with topographical functions in different fields of science and engineering. The shallow water 2D equation was used to model the coupled dynamics of surface and subsurface flows. These equations form a system of coupled nonlinear partial differential equations. The development of an easy-to-use and robust numerical method to accurately determine fluid motion in this coupled flow scenario, including topographic considerations, is of utmost importance. The numerical simulation results of these equations are obtained explicitly using two numerical methods: the forward time-centered scheme and the Lax-Wendroff method. This study compares the numerical simulation results of the connected region at different time steps. The stability is checked through error analysis. Both methods give identical numerical results, although the Lax-Wendroff method shows a slightly better performance. All these numerical results are obtained using CFL stability criteria.
Keywords: extended shallow water equation, forward time central scheme, the Lax-Wendroff method.
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