Numerical modeling of passive scalar transport in shallow water based on the quasi-gasdynamic approach

A new method for the numerical solution of the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is based on previously developed quasi-gasdynamic algorithms for numerical simulation of compressible gas flows. Smoothed equations are derived, and their difference approximations, including for flows with a pollutant source, are presented. The numerical algorithms are tested as applied to one- and two-dimensional flows. As an example, the algorithm is used to solve the problem of water circulation in Lake Vallunden. The constructed approach is generalized to passive scalar transport in the case of viscous incompressible flows.