Использование адаптивных сеток при решении двумерного уравнения неразрывности полулагранжевым методом

We develop a semi-Lagrangian algorithm for solving the two-dimensional advection problem. A numerical solution is constructed as a piecewise constant function on neighborhood of grid node. The proposed method is stable and gives an approximate solution with the first order of accuracy for smooth solutions. We use dynamically adaptive grid. As initial guest we consider rectangular grid.