A Semi-Lagrangian method on dynamically adapted grid for two-dimensional advection problem

摘要

We develop a semi-Lagrangian algorithm for solving thetwo-dimensional advection problem. A numerical solution is constructedas a piecewise constant function on neighborhood of grid node. Theproposed method is stable and gives an approximate solution with thefirst order of accuracy for smooth solutions.We use dynamically adaptivegrid. As initial guest we consider rectangular grid.