Propagation of diffusing pollutant by kinetic flux-vector splitting method

In this article, the transport of a passive pollutant by a flow modeled by shallow water equations is numerically investigated. The kinetic flux-vector splitting (KFVS) scheme is extended to solve the one and two-dimensional equations. The first two equations of the considered model are mass and momentum equations and the third equation is the transport equation. The suggested scheme focuses on the direct splitting of the macroscopic flux functions at the cell interfaces. It achieves second-order accuracy by using MUSCL-type initial reconstruction and the Runge-Kutta time stepping technique. Several numerical test problems from literature are considered to check the efficiency and performance of the scheme. The results of the proposed scheme are compared to the central scheme for validation. It is found that the results of both the schemes are in close agreement with each other. However, our suggested KFVS scheme resolves the sharp discontinuous profiles precisely.