Conservative second-order monotonic numerical method for solving two-dimensional continuity equation

Abstract The paper demonstrates constructing monotone difference scheme for the two-dimensional (in space) transfer equation in divergent form by the Lagrangian–Eulerian approach. It is based on the use of spatial grids formed by the approximate traces of the characteristics for this operator. The use of such special grids made it possible to circumvent the limitation by S. K. Godunov on the absence of monotone schemes above the first order of convergence. A brief theoretical justification for the second order of convergence and supporting results of the computational experiment are presented.