Modelling of coupled surface and subsurface water flows

TL;DR

This paper introduces a numerical scheme combining HLL finite volume methods with implicit techniques to accurately simulate coupled surface and subsurface water flows, accounting for complex source terms and infiltration processes.

Contribution

The paper presents a novel second-order accurate numerical scheme for coupled surface and subsurface water flows using HLL finite volume methods with well-balanced discretization.

Findings

Successfully simulates coupled water flows with complex source terms

Achieves second-order accuracy in numerical solutions

Demonstrates effectiveness through numerical experiments

Abstract

In this paper, we propose to use the HLL finite volume scheme combined with implicit techniques for modelling the coupled surface and subsurface water flows. In our approach, we used the shallow water equations modelling surface water flow with different source terms such as variable bottom topography, friction effect, precipitation and infiltration. For subsurface water flow, the Green-Amp equation is used to simulate the infiltration process through soils. For solving the resulting nonlinear-coupled system of shallow water flow and the Green-Ampt infiltration equations, the HLL finite volume schemes with linear reconstructions of the solutions at the discrete level are implemented in order to achieve the second-order accuracy of the scheme. Appropriate discretization techniques are used for the source terms to guarantee the well-balanced property of our numerical scheme. Numerical experiments are performed to test the capability of the developed numerical scheme to simulate the coupled surface and subsurface water flows.