Weighted Essential Non-oscillatory Schemes for Simulations of Shallow Water Equations with Transport of Pollutant on Unstructured Meshes

In this paper we study the third-order finite volume weighted essential non-oscillatory (WENO) schemes to solve the two-dimensional shallow water equations with pollutant propagation on unstructured triangle meshes. Balance of the flux and the source terms make the shallow water equations fit to non-flat bottom problems, in order to maintain genuinely high order accuracy and suit to questions with a rapidly varying bottom topography we use WENO reconstruction not only to the flux but also to the source terms of a algebraic modified shallow water problems. Simulations are performed, as a result, the finite volume WENO schemes can maintain non-oscillatory properties and achieve high resolution.