Hasan Karjoun | Searcharxiv

arXiv2021

Modelling of coupled surface and subsurface water flows

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.

math.NA↗

arXiv2020

A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport

We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization techniques are proposed for the water surface elevation and the concentration of the pollutant. For the hydrodynamic system, the proposed scheme preserves the steady state of a lake at rest and the positivity of the water depth. For the scalar transport equation, the proposed method guarantees the positivity and a perfect balance of the scalar concentration. The constant-concentration states are preserved in space and time for any hydrodynamic field and complex topography in the absence of source terms of the passive pollutant. Importantly and this is one of the main features of our approach is that the novel reconstruction techniques proposed for the water surface elevation and concentration satisfy the discrete maximum-minimum principle for the solute concentration. We demonstrate, in a series of numerical tests, the well-balanced and positivity properties of the proposed method and the accuracy of our techniques and their potential advantages in predicting the solutions of the shallow water-transport model.

math.NA↗