Regularization method for numerical modelling of a transport of pollutant in shallow water

A new method for solving the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is similar in structure to the previously constructed quasi-gas-dynamic algorithm for the numerical simulation of compressible gas flows. Regularized equations and difference schemes based on them, including those for flows with an impurity source, are presented. Typical one-dimensional and two-dimensional test problems are considered. In conclusion, a generalization of the constructed approach for the numerical simulation of the passive scalar transport in the framework of the viscous incompressible fluid approximation is given.