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We present a new one-dimensional hybrid second-order accurate well-balanced unstaggered central scheme/particle method (WBUCS-P) for computing the transport of pollutant in water flows. The shallow water equations are employed to model the free-surface water flow, and the transport equation is employed to model pollutant propagation. Our proposed scheme employs the particle method and avoids the resolution of Riemann problems occurring at the boundaries of neighboring cells. Furthermore, the proposed hybrid method is second-order accurate both in space and time; it evolves a piecewise linear numerical solution on a single grid, and benefits from the non-dissipativeness property of the particle method. Our scheme is also well-balanced due to a unique integration of the source term and to the application of the surface gradient method. We implement the proposed scheme and solve some selected problems featuring the transport of pollutants. Accurate pollutant’s location and concentration are observed and reported in the numerical test cases. |
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