Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations

Abstract

We present in this thesis a new well-balanced unstaggered central scheme for computing the transport of pollutants in water flows. The shallow water equations are used to model the water flow, and a transport equation is used to model the propagation of the pollutant. Our proposed scheme avoids the resolution of Riemann problems arising at the cell interfaces; it is second order accurate in space and time, evolves the numerical solution on a single grid and benefits from the non-dissipativeness of the particle method. Our scheme is also well-balanced due to a special discretization of the source term with the surface gradient method. We implement the proposed scheme and solve some selected problems featuring transport of pollutant. Accurate pollutant’s location and concentration are observed and reported in the numerical test cases.